I spoke to CLSG ages ago about their 7+ and 11+ entries when it looked as if we would get a primary school I didn't have a great deal of confidence in.
Their advice was that they didn't particularly like kids to be tutored, but in the case of children coming from state primaries, they may well have not covered the syllabus for the exams. While they do make allowances for children coming from the state system, if they can't answer the questions then they can't score the points.
Therefore it was acceptable to tutor in English and Maths and do a few VR tests so that the child was familiar with the format. But tutoring for interviews was a big no-no and was generally obvious.
They certainly used to have past papers available on their website.
I can't help regarding tutors as we're not at that stage yet. You might find the 11+ forum useful. Depending on how much help you may feel you need, it might be worth making enquiries with a few to see what their advice is with booking - imo, better to know in advance rather than be struggling to find one last minute.
Plenty of people do tutor themselves, but it does depend on how confident you are and the kind of child you have. I have a suspicion that if I try and tutor DD it will end up in a massive battle of wills whereas she'd respond better to an outsider.
Regarding art - I would be very wary about having tutoring in art until she is much older. I'm a designer/illustrator and went to art college. My dd is better than I was at the same age and I imagine will be good at art later. She watches me and asks how to do things and I won't teach her.
IMO - and many may disagree with me - teaching technique too early can massively impact on innate creativity. Around 8 or 9 you can begin introducing the concept of shading or perspective, but not before then. I hate programmes like Squiggle Bits that show children the 'right way' to draw things. I believe that everyone has the ability to draw well, but many are put off by things not 'looking right', get frustrated and give up.
The best thing is to take your child to galleries to expose them to a wide range of art and discuss what they like, don't like, types of paint etc. I have a huge box of art 'stuff' - feathers, bits of coloured and sparkly sweet wrappers etc, big packs of cartridge paper and sugar paper. Lots of pencils, pens, paints, glue etc and I just let her get on with making things.