I think there's a massive difference between adopting a more relaxed approach in some areas and 'no rules'.
I've always understood that rules make children feel more secure (as bizarre as that sounds). Googled quickly before writing that and it comes up with lots of hits you might like to read (I searched on 'do rules make children more secure?')
I also think that as parents, our job is to prepare them for their life ahead. If your child isn't encouraged to follow rules at home, what will happen at school? Or at friends' houses? When driving? Or later on at work?
Maybe consider how you 'pick your battles' - which areas need rules and where can you chill a bit.
Also some things might vary - so not having a rigid bedtime might be ok during the long summer holidays, but would you want her going into school tired?
She's young enough to possibly benefit from a reward chart or similar to encourage her to do things like clean her teeth and brush her hair.
Re food, I think you put fruit and veg out at each meal but don't make a fuss. Over time she'll probably try things if it's not a battle ground. If she's not having much on some days, I'd put some vitamin drops in her drink (without her knowing so she doesn't see that as an easy way out).
Others may not agree with what I've said but that's the thing about being a parent, we have to decide what we think is important for us.
I'd consider what everyone has said on this thread before adopting a no rules approach - might make for an easier life now but I think you would be storing up trouble for the future.