I'm not much an expert, but i will try to answer your question:
1) while i cannot judge your rabbit's age just by looking at their photo, i strongly suggest you should go back to the pet shop or their previous owner to enquire, as this is a very important aspect for their diet regime, health issues and training;
2) diet: young rabbit until the age of 3 mths should be only be fed with with alfafa hay and a handful of pellets; why alfafa hay? bcos young rabbit need those extra protein, vitamin and calorie to grow; after abt 3mths, you can give some vege. generally dark leaf vege is ok; as it is lower in moisture content and more vitamins. avoid vege with is high in moisture (celery, lettuce, etc..) and 'gassy' vege (cabbage, brocolli, cauliflower, asparagus, etc); and yes, you can feed them flowers too, but be careful of the pesticide most flower does. then, at the age of 7 mths only you can introduce fruit (any non watery fruits like apple, guava, etc.. if feeding cucumber, pls ensure the seed part which is watery be removed) and root (must be careful to avoid 'starchy' and fatty food like all type of potatoes, peanuts, corn, etc) to them. but they do love carrot and red radishes. avoid 'white' radish as the taste is stinging them.
3) diet is one of the 2 important aspect of raising a rabbit as they are known to have delicate digestive system and this is one of the common reason why they died. remember they cant bark or whine, so it's not easy for you to see whether they got problem or not.
4) to answer some of your question:
a) the reason your rabbit dun take much alfafa hay or any hay at this moment is bcos they have ample of 'fresh' food, which is tastier; imagine you are your rabbit, you want to eat toasted bread or char kuey teow for breakfast? haha.. and one thing most ppl doesn't know, rabbit just like gold fish, they are not as intelligent as cats and dogs (so to speak) to know when they are full or have an instinct to avoid those food which is harmful to them. if you are continuing feeding him/her like what you are doing, there are only 2 consequences; either they will die or they will survive, but chance for the latter are very slim.
b) you are right (partial)! pellet shall be their main staple with with vege, fruits, carrot, etc ('fresh food') shall be the 'treats'. generally their diet should consist of 80% hay, 15% pellets and 5% treats. they need to chew on the hay to to wear off their teeth and if you give them too much 'treats'; training them will be harder than ever (remember you need this to potty training, hurdles traning and if you are patiently enough to train, they can come when called their name! just like a dog!).
c) it's not like they do not know how to use the bottle, but they don't need it, cos they are getting most of the water from the arrays of 'fresh food' you fed them; while i know some owner did give their rabbit water bowl, but it's not highly reccommended as the water will make their fur entangle accidently.. so once you switch their diet, they will drink like a camel..
d) rabbit harness are plenty available at pet shop safari (if not mistaken) in sunway and the curve (try google them around) at rm35 each.
Sorry, i did not intent to write this long originally; i could have bla bla bla more on their health issue and training, but i bet you are sleepy already.. haha.. i hope you have a healthy and bubbly rabbit like my 'bit bit' (he is about 8yo now and still healty as ever!)