- 7 can lights
- 120v water heater
- 5 outlets
- bathroom GFCI
- exhaust fan
- Mini-split heat exchanger
TL;DR Yes, but...
Keeping in mind that 50A is 50A @ 240V, which is 100A @ 120V, and most of your loads are 120V, that should be plenty:
- 20A 120V bathroom
- 20A 120V water heater
- 20A 240V mini-split (there are a lot of options, you might not need this much power, depending on house size and HVAC efficiency)
- 20A lights/convenience receptacles
However, the formal way to do this is a Load Calculation. And there is one key piece that you are missing to turn a tiny house into a functional "home": cooking appliances. Electric cooktop, oven, microwave oven - anything will use a good bit of power when running. So that's the key missing link to see if 50A is really enough. Comments indicate no real cooking appliances, so this is probably OK.
As Harper already noted in a comment, once you get past 30A, switch to aluminum wire, and with aluminum wire there is usually good price on 2/2/2/4 cable that is good for up to 90A. But be careful: before jumping to "OK, I'll put in 90A and have more than enough for anything" (well, except tankless hot water or unrestricted EV charging), you have to do a Load Calculation at your main panel/utility service to determine how much power you can spare for the tiny house. If you have 200A service and not too much stuff, 50A or 60A or maybe even 90A will be fine. If you have 100A service, or if you have a lot of big electric appliances in the main house then you may have a problem.
Comments indicate the existing panel is FULL. That doesn't necessarily mean anything, but consider the checking account analogy: If you run out of checks (breakers), you haven't necessarily run out of money, but if those checks you wrote were for large amounts then maybe you did run out of money. So a formal Load Calculation of the main panel is important. In addition, a picture of the panel might help identify some potential safety and/or usability issues.