Could you help me out?

Hello all, just wondered if anyone cud help me out with a few questions.

I let me hen out each morning and then i have her back in her coop for about 3pm as my mother in law who previously kept chickens sed this is the time that the fox likes to venture out. Is this ok or should i be leaving her out for longer?

Im cleaning the coop once a week and putting fresh bedding in etc is this ok or shud i be doing this twice a week or more?

Ok i think this is going to be a stupid question but here goes, do you bath you chicken? Im only asking because theres a bit of muck near her vent so i was just wondering if i could do anything to tidy her up.  

Im feeding her layer pellets, is there anything else i should be giving her, how often and should i be taking her food off her during the day and giving it her in the evening so she'll come into her coop?

Thanks to all info and advice it really is appreciated.

Foxes are getting more adventurous. We live in the country and one has had chickens at 4 pm under the nose of a dog and another at 2pm immediately after they were let out, so a fence is good. Foxes will get through a thin fence at night, but during the day they need to be able to make a dash for it.
If you bathe them, they'll love it. No need to do head to foot, but sit them in warm water and they soon relax. After a few moments, the poo loosens and I use a kitchen sponge to just finish off the job. In cold weather blow dry. Cut corner off sponge so it is recognisable and never wanders back into the house.
Always leave food and water available throughout the day. Have fun.