How exciting! Best of luck to you. It's a great list of questions and shows how much you've thought about it. Here's my advice based on what I think I would want if I were auditioning someone:
1. What to wear: This is nowhere near as important as you think it is! The MOST important thing is to be comfortable and to wear clothes you can move in easily. Think about whether, when you move, you are likely to expose bits of your body you would rather were not on display! This is particulary important if you're wearing low-slung jeans/trousers. It's really off-putting for someone observing you if they see you constantly hitching up your trousers to cover your bottom. This is really common.... Also consider whether you'll be flashing a lot of cleavage when you lean forward! Otherwise, plain or bright is up to you really. I'd just concentrate on clean, not too fussy and comfortable. Probably best to avoid really busy patterns - they can sometimes look odd on camera and are in any case a bit distracting for someone watching you (you want them to watch you, not be mesmerised by your clothes). You definitely don't have to wear what you wore in your photo (though you can if you like!). In some cases, it can be useful to think about the character and to try to ensure that you don't wear something that is the direct opposite of how you think that character might dress. Don't get too hung up on this though. I usually think of it like this: "if I were this character and I had to choose something from the clothes in this wardrobe, what would I choose?".
2. Yes, it's a really good idea to get there early. If you're like me and get there super-early (like an hour before

), you can always work out exactly where it is and then go and get a coffee, go to the loo etc and then go back 15 minutes before your audition/appointment time. Be prepared to wait longer than this - sometimes these things over-run.
3. In the improvisation you'll need to be guided by the person doing the audition. "Improvisation" can mean a multitude of things. They may well ask you to imagine a scenario as if you were the character you are auditioning for (this is likely, but not certain) in which case the answer is obvious! If the improvisation is more general, then no, ditch the character and go for whatever the improvisation demands. It's hard to prepare for improvisation, so try not to worry too much about it and go with the flow! Try your very best not to let nerves stop you listening to what is being asked of you. Don't be afraid to ask for clarification if you don't understand something. They want you to be able to do well. Make bold choices. If you are asked to try something that sounds a bit weird try to go for it wholeheartedly. If this is for film or TV try not to "project" to an audience, try to keep it as real as you can.
4. the mascara thing.... I'd advise no mascara. You want to give yourself every chance to look young. If you really can't face doing it without, you might like to consider brown mascara which isn't quite as harsh. I'd still advise doing it without...
Like the clothes, this won't be make or break though, so don't fret too much!
Unless, that is, they have asked you to come without make-up. If they have, please, please take their request seriously. If they have asked, it's because it matters to them and if you ignore their request you - well, that means you are ignoring their request and that seems daft! Why give them the chance to think "Hmm, took no notice of the no make-up request then. Vanity? Is how she looks more important to this actor than the job" ?
5. They will certainly want your Mum to stay outside the audition room, though there will probably be somewhere she can wait that's really nearby. If you mean, do you have to go into the building alone, then I think this is up to you. I don't think you'll be judged either way. I think if I were you, I'd go into the building with your Mum in case there's anything she needs to sign.
I hope all that's of some help. General tip is: be pleasant, open, honest and friendly. Don't feel you need to pretend to be anyone other than who you are or that you need to pretend to have more experience than you have. They have called YOU in. That's who they want to meet!
Best of luck