That is absolutely fine to ask to go back for a look during a working day - although be prepared the place might be a 'mess', noisy, the minder won't have time to talk etc, so it would be a 'quick' visit iyswim.
Again absolutely to references - however if they are a new minder they may not have any.
The minder may have a portfolio/scrapbook for you to look through. Feel free to ask questions.
What should you be looking for:
someone you feel comfortable with
someone who takes an interest in you and your child
is open and welcoming
homely environment - with a good bank of resources and equipment (again if they are new they many not have loads), ask about routine (ie school runs, when meals/snacks are etc), what activities they do, where do they visit (ie soft play, library, shops, other mindres, children centers etc)
are there any extra charges: meals, outings etc what do you have to provide/what does the minder provide (ie nappies, meals, etc)
what about bank and public holidays
childminder holidays
do they have back up minders or a good network of minder friends who you.she could approach for alternative care if she is off
how many other children does she care for
be clear about the hours and days you want
they should have a list of policies and procedures and talk you through the more important ones such as safeguarding, equal opps, fees and charges, complaints - however they may not bombard you with all this informtation just yet
they should allow you a guided look around the house
how much outdoor play/opportunities and also social opportunites (beware of the minder who is ALWAYS out though - childminding is about home-based childcare meaning being at home some of the time).
pets/other household members
how that minder is going to settle your child in - many offer a few short pre-starting sessions
goes without saying when you find one - you should complete a contract, permissions etc - make sure you read all paperwork before signed and agreeing
many minders will ask for advance payments/deposits be honest if you cannot afford what they are suggesting some are willing to negotiate.
with a minder that is right for you - you should feel at ease with them
Visit several minders until you get a 'feel' for one.
good luck