Hallo, Anna!
First of all, as Jim told you, please do find the time to read the relevant articles in the Library section. There you'lldiscover everything you need to know about a healthy, balancedand proper diet, as well as suggested quantities.
In short, to answer your specific questions, the basis of a good diet is, indeed, unlimited hay. Jamie should have fresh, nice smelling hay available 24/7. The second element should be high quality pellets (i.e. containing fibre from 16% upwards, the more fibre content, the best, fat up to 2.5%, proteins up to 12.5% max. If you read on the pellet box the guaranteed analysis, i.e. what the pellet is made of, you'll find the above data) and thirdly a variety of leafy greens. Lettuce (give only the dark leaf one, not romaine and not iceberg lettuce) is high in water content, but doesn't contain a lot of nutrients, so you should give a wider variety of greens. Please remember to add one different species of veggies per 2-3 days and keep the quantities fed low at the beginning. Add a bigger quantity and variety progressively over a period of 1.5-2 weeks, to avoid GI issues.
Look at the "safe vegetables and safe fruit'' lists in the library to get an idea what could you safely feed your bunny. Fruits and herbs are safe treats. You should give veggies in moderate quantities and fruits only as a treat, i.e. a thin slice every now and then. Buns love banana but it is high in sugar, as carrot is also, so don't give them every day.
You are right about commercial treats, they should not be fed. Yogurt and yogurt drops are a big NO-NO, they can potentially create GI problems.
Please go check the library articles and, if you have any queries on what you read, we'll be happy to answer them and clarify whatever you may not understand.
Marietta