I know, you feel selfish to "ask" for gifts, but they will be bringing a gift, just tell them what your child enjoys and they can choose what they would like to get her and what they can afford in their budget. I really wish parents would just open their mouths and tell you, so it's not a guessing game and you can get the child something they will use and enjoy. She really enjoys Littlest Pet Shop or Polly Pockets and playing dress up or playing cars or coloring. My kids are older and the things they want are kind of expensive. I wouldn't expect a parent to spend a lot of money on a video game, but I could say to people who inquire, a gift card so he can buy a video game would be or a gift card for laser tag or iTunes something. I've had parents tell me the kid likes the clothes from such-and-store, so anything from there or a gift certificate would be great.
Try not to feel so selfish over this. They want to know, so they they buy something your child will use and enjoy and they can spend whatever is in their budget. Just toss out some ideas your child enjoys and they can pick what they would like to give. If they ask, you could tell them that you're not expecting gifts but little Morgana loves playing princess or loves Dora the Explorer.
As for the invitation, it's for a 4 year old, and they're going to expect it to be geared as such. Just put the time and number. Some of the invitations we receive have the home address, some don't, so you have to call to get that information. I would prefer the address be included, so I know where I'm going. If people live too far away, I might not say yes. If you have any special requests, put that on there, like "bring a swimsuit," or something. If you're planning this party at a venue like Chuck E. Cheese or goofy golf, include the address on the invitation and even a map or directions. My child was invited to laser tag, and included on the invitation is proper clothing they need to wear and that parents will need to sign a waiver, which they can print up themselves, or they'll have to fill it out when they drop off their child.