Welcome to your new little girl!
I agree, and recommend you give her a bowl of her own. Doesn't have to be a major deal. Just a 2.5 gallon bowl will do very nicely. No need for filters or air pump. A mini-heater would be nice for the winter especially.
My female eats the same as my boys. Hikari pellets with occasional live food lately (so far brine shrimp and blackworms. both were big hits).
It is normal for bettas to lay on leaves of plants. Sometimes you are think they're dead because they're in such a weird position. But they like it. That's why I try to put several different plants in there for them at different heights.
Although I have some males in bowls, my girl has her own tank. She's in a 6 gallon eclipse. She's my longest lived betta so far, I've had her for about 26-28 months (not sure how old she was when I got her but she was still kind of small).
Just to let you in on my girl's story......
I originally got 3 females. I watched them at the store that had several in a small tank and picked out three that seemed to get along very well. The tank I put them in was a little larger and had more plants and hiding spots so I thought they'd do great. I watched them closely to see if they were getting along. I noticed one of the fish seemed to be a bit more of a bully but only some chasing, never attacks. I figured that they'd work it out, one would become Alpha Fish and everything would be ok. Well, I think there was more stress than I realized. After about 2 months I lost one betta. Another month or so later I lost the other. I've never had bettas die so soon, usually they last a while with me. I felt so guilty. I thought I was watching them so closely. Neither of the fish ever showed any signs of damage at all so I don't think there was ever any contact. Somehow Athena just "vibed" them to death or something. Since then she and her pet snail have been living a comfortable life in her luxury home. I've been kind of afraid of putting anything in with her. Although, last week I just got a kuhli loach and put him in there with her. We hardly ever see him so it's as if she were still alone. She did watch him with interest when he came out the other day. Nothing else, just parked herself and watched. Maybe she's mellowing in her old age.