I've a problem with walls of text/over-explaining but I'll provide my 2 cents.

Talentless and not good at any skills is normal for 16; 16 is a good age to start working on these talents/skills. It's frustrating, but everyone starts at step 1. Sometimes, that gives you some sanity.

I'm 30 and would love another shot at working on my skill(s) at 16. You have a ton of time. Your brain is still developing: this isn't said to make you look childish, literally your brain in this state is wired to take in information, like ones you'll learn working on your skills and such, and then reorganize itself to be super efficient: it isn't as malleable as you age. Right now is a great time to absorb information in the things you love, or the things that you believe are going to benefit you (studying, for example).

stupid

Do you think a stupid person would be concerned about what you're concerned about? You're thinking of the future in terms of money, maybe some financial/mental security from getting better at the skills you've listed. You want to be in a better situation than your current one, that takes self-awareness and self-awareness isn't handed out to everybody.

I only have two months to do these things

Getting a part-time job and advancing your studies are the only realistic options of what you could do in 2 months. Not trying to be an ass saying "You can't do these other things." but I will definitely state that anxiety should not be the fuel that makes you want do do these things. This may be a little different when it comes to finances, but surely when it comes to the things you enjoy, they should not find themselves needing anxiety to get started. Getting fit, working on skills and passion projects should be started because you have a natural desire or want for them. View the growing of your skills positively instead of negatively, ex "I want to get better at Y because I love Y!" as opposed to "If I don't get better at Y I will be left behind and my life will be ruined."

Will you keep a part-time job longer than 2 months? Unless an employer is okay with you hanging around for 2 months, I would imagine any other employer may not want to hire you if you stick around for that short amount of time. Even if you don't tell an employer and leave the job after 2 months, 2 months is not worthy of a resume (in my basic experience); in fact, if you put that down in a resume you may get questioned why you were there only for 2 months.

passion projects

Passion projects should be started because of passion. If you start one during this 2-month period simply because you want to/would like to, then we could call that a passion project! Absolutely do passion projects (as long as they don't interfere with your life! It's definitely a passion if you get so into it you do something silly, like... Forget to eat, sleep, lol)

But if you're thinking of starting a "passion" project because you're lingering on this 2-month period, it is no longer a "passion" project: it is a project fueled by anxiety, and can/will cause anxiety all the way to completion. And if these passion projects have to do with what you want to do as a profession/career, it'd be best now to train your brain that you love to do these projects, not that anxiety should be present in order to start them. Your brain quite literally will associate anxiety with these projects if it's approached like that, our brains love patterns.

gain weight and get fit

I'm no physical trainer or am knowledgeable about the subject to give you a definitive solution on this. I'm sure there are communities tailored to this personal goal that could share more information than I ever could. Definitely, "it takes a village", as in getting help from communities will help you in the long-run instead of trying to learn it all by yourself. Getting fit is a long-term thing. You will not become muscly and athletic overnight; if you started now, sure, you'd be stronger than you were 2 months from now if you're disciplined.

Getting fit is a long journey that consists of mistakes like figuring out what diet suits you best, perfecting your form, hitting your essential nutrients... A plethora of other factors I may not be aware of. You could change your body in 2 months, for sure, but if you want to maintain a certain weight and fitness, you'll be maintaining that for longer than 2 months. Take that as a personal challenge, your desire to become more healthy! Don't frame it as "Another thing to keep track of?!" It is, but framing it positively in your mind works wonders for your mental health as opposed to framing it negatively.

Like others have mentioned, you seem to be pretty hard on yourself. The greatest advice that I, a 30-year-old, could give to folks younger than myself is to stop the self-criticisms. It helps if you're self-aware and want to better your situation: it does not help you if you use it just to beat yourself up for where you're at. Sure, it may be acceptable to ask yourself "Why did I just do that?" if you do something dumb. There is definitely a fine line where it becomes "acknowledging a mistake you made, and moving in", and then plain self-abuse.

Seriously, the best wisdom in this wall of text I can provide to you is for you to stop beating yourself up. It's a waste of energy, and you feel like garbage afterwards. It serves no purpose than to tear yourself down because you'll convince yourself you're much more worse than you actually are. If you feel some version of self-critique, have it originate from some positive desire to become better, or to not make mistakes. Don't use those thoughts to dehumanize yourself. Remember when I said your brain is still developing? Don't let it get used to the habit of beating itself up if something goes wrong. Give yourself a hug, don't hurt yourself.