My question is about using a stage name.

My last name is long, nobody can pronounce it correctly, and to be truthful I don't care for it much. I am wondering if to use a stage name do I have to legally change my last name? If not do I have to explain to directors etc. that it's only a stage name? Thank you very much for your help.
You do not have to legally change you name. However, if you choose a stage name that a professional actor already has, you would not be able to use it if you ever hoped to join an actor union and get paid for your acting work. So choose carefully. You do not have to mention that you are using a stage name. However, if you get paid, you will have to make sure your checks are made out to whatever name you use for your bank accounts and that you don't run into mix-ups with social security and taxes. Talk to your bank about setting up your accounts to make that possible.

I've seen and heard countless times that it's taboo to, on an audition, sing a song from the show you're auditioning for.

However, I have an upcoming audition for a play that the casting notice requests actresses going for the lead to play 16 bars of a piano piece if they choose. I read the play and realized that the lead plays a specific (and somewhat recognizable) Nocturne by Chopin. I know how to play piano, and I know 16 bars of this piece, so I suppose my question is... would you recommend I play the piece that will be in the play, or should I play something else? Thank you so much in advance for your reply, and have a lovely rest of August!
Go ahead and play the Chopin piece. In case they ask, be prepared with a couple of others to play as well. Demonstrating to the auditors that you can play the piece is different than performing with a song from a play. They will likely be happy to know you indeed have the ability to satisfactorily play Chopin and will be in your favor. 
BTW, unless specified in the audition notice, it is OK to perform a song from the play for which you audition. If the auditors happen to like your rendition, it will build interest in you for the part (or another part.) If they don't like it (they might have a rather specific, preconceived notion of what the song is supposed to sound like) it might cast a bit of a shadow. If you are unsure, ask. You should always be prepared to sing an appropriate, alternate song.
What is most important is that you do not simply "sing" the song. The song is designed (usually) to propell the character development and plot along. So the song is "acted" (like dialog) - the actor must convey motivation, subplot and all those other good actorly things. Break a leg.

If you think you might be too old to get into acting...

It is never too late to start acting. However, your chances of earning a living as a professional actor are extremely small. Of course this is the same for just about anyone who wants to become a professional actor. Take a look at the AWOL lesson, AN ACTOR'S LIFE... on the AWOL homepage.
 
If acting is something you feel driven to do, I suggest you take some classes and get involved in community theatre and whatever local film, TV and industrial productions you can find. This will help satisfy your creative desires and earn you a few dollars once in a while. Who knows, after awhile, things might lead you in a professional direction after all. Just don't quit the day job yet.

Considering how competitive the business is and how many actors have a big training and experience jump on you, you will have to be quite focused and work hard to get trained, develop experience and learn about the business. You should not wait any longer to prepare yourself to compete. This means lots of workshops, classes, auditions and reading every acting book you can find. It means classes in singing, dance, literature (even poetry), music, improvisation, etc. It means a lot of hard, focused work.

How do you make yourself cry?

Here are my best thoughts on crying. If you are having a difficult time crying in a performance, then the problem is with your acting technique, not your crying technique. Which is why you are having such a hard time fixing it. You are trying to correct the wrong thing.

Don't try to develop some mechanical technique to make yourself cry. Your character, in the context of the play, isn't using some technique to make himself cry. The conflict or release of conflict within the character, intentions, etc. is making the character cry. If you focus your attention on a mechanical technique, or focus on some imagined, out-of-script sad event, then you are no longer focused on your character. Your mind is not on the character and the circumstances. Your mind is now on the actor trying to cry. Not the character, thinking, remembering, desiring, reacting, feeling the urge to cry, resisting the urge to cry.

Focus on your character and in playing the moment believably. Focus on the through-line, subtext, intentions, timing and all that other acting stuff (see the FREE Acting Lessons on the AWOL homepage .) If you did your job well, the tears will be there when they are supposed to be there. Why? Because if it is believable that the character should cry, and if you are fully absorbed in playing the character, then you will cry.

What if you are not fully absorbed in playing the character? The stage is not so predictable performance after performance. For camera work, take after take. What if the tears don't come? If you are doing your acting job well, then don't sweat the tears. Heck, most members of the audience will swear you actually cried even though you did not. Why? because your belief in the character becomes their reality. That's the magic of acting.

For camera work, if all acting efforts fail, the closeness of a shot and the level of "realism" required might indicate other measures be taken. The director simply shoots the scene without your tears, cuts, places some fake tears on your face and shoots the scene again but from another perspective, then edits the two shots together melding the moment just before you were supposed to cry with the moment you began"crying"with the fake tears in place - to make it appear as if you cried real tears. The different perspectives cover for the fakery - just like it does with the other thousands of edits which make up a film. You can cheat a lot in camera work.

I just recently attended an open call for a model/talent convention...

...and have been selected to attend. I am pretty excited about this. The people who selected me told me they believed I have what it takes, and the agents would be really interested in seeing me. I am interested in your advice regarding attendance at this convention. They are asking for a lot of money to attend. Is it worth the money invested? Is this a good way to get into the modeling or acting business?
Model/talent conventions are a terrible way to try to get into the modeling or acting business. 
They are expensive and yield little of value. They are scams. They are scams because *MOST* (almost all) of the people who attend such events receive little of any real value for their money. A few workshops, a quick walk on a runway and a "chance" to be seen by "agents" is hardly worth the many hundreds - even thousands - of dollars these ridiculous model searches charge.
All legitimate modeling agencies hold open calls at their offices - at NO CHARGE!!! Just call the agencies and ask.
The people who organize model/talent searches are fully aware that over 95% of those who attend will not be "chosen". 

They are fully aware that of those who are "chosen", only a few might actually gain any significant work on any regular basis.
The people who organize these searches take in hundreds of thousands of dollars in fees. Almost all the people who attend receive little of any value toward a professional modeling or acting career.
Model/talent conventions are scams.
The information you provide to the "professional scout" (usually someone who knows little if anything about the modeling business) at the model/talent search "open call" was likely sold to modeling and acting schools, photographers or anyone else interested in selling services to naive but eager model/actor wannabees.
The "scouts" are trained to get as many people to pay to attend the search as possible - whether the attendees shows any merit or not. The scouts use a lot of flattery and misleading statements to accomplish this goal.
The agents who are at the search are paid a sizable fee to attend. Many of the "agents" are not really agents. They are agent assistants or other people who have no decision making authority and lack the ability to actually sign an attendee.
Often times, the staff of these searches and even the "agents" use the open calls and the search convention to find cute women and men to "date" (have sex with). This will not advance anyone's chances of launching a modeling career. It just makes fools out of the attendees.
The organizers usually require agents to "callback" a certain number of candidates, whether they are interested in all the candidates or not.
A callback does not mean you have been "choosen" or are on your way to a career. It simply means that the "agent" wants to talk to you again. Most attendees who are called back do not ultimately receive any representation.
There are far-far better, less costly and more productive ways to get into the modeling and acting business.
I suggest you head to the library or spend $20 or $30 at your local bookstore and get a book or two about the modeling and acting business so you can learn something about how things really work. It is far, far cheaper than wasting money on silly model/talent searches.
For more info about acting and the acting business, see this website:
http://www.redbirdstudio.com/AWOL/acting2.html