Hello. I wonder if there are any psychologists, amateur or professional, or just someone with casual interest or experience, who can tell me what might be going on with a girl I just met.

It's only been three days. I was sitting in a café in London and this pretty, well-dressed girl starts smiling, flirting with her eyes, checking me out, and then asking me the time, and then more, until we're talking. She's 28 and old-school London 'posh'. She does seem odd - slightly mumbly, giggling a little to herself in the gaps - but odd has never really bothered me. In fact I find it interesting and, if I'm honest, sexy. So before she leaves, I get her number.

By the next day we're meeting up. She's staying in a hostel (has had some kind of row with her parents), so I know she wants to stay with me and that it accounts for part of her interest. But she does also like me - compliments my looks, tells me I'm lovely, holds my hand/arm as we walk (yes, a bit sudden, but not too weird really and, as I say, quite nice). It's the other stuff that's slightly unnerving.

• The giggling. Sometimes in response to questions, sometimes when there's silence. Understandable in an awkward situation, and she does refer to it as having the giggles, but it's still unnerving and, in a way, somewhat insulting.
• Repeats the same question two or three times after I've answered it.
• Quite distracted - not really present. I thought at first she was stoned or high, but I don't think so. She's just quite far away.
• Her answers and statements are so vague, contradictory and mumbled I feel constantly like I want to make her say more, or clarify, but I don't want to annoy her.
• Quite racist. At random, incongruous moments. "I mean there's only so much f*cking land" etc, and, "So how long have your parents been English?" And much worse.
  
• Random statements at times. Almost like she's speaking for the sound of her voice than to convey anything. Strange, unrelated subject matter will pop up (a food item, for example). She'll follow it with a giggle, like she knows it's weird.
• Mild OCD. Lots of hand washing, tidying, trips to the loo. If she touches an everyday item, she'll wash her hands.
• Not clingy - that is, she goes away when asked - but after two days is already talking about moving in, being my girlfriend etc. I know it's partly her accommodation problems, but I also know she likes me.

I suppose they don't sound too strange in isolation, but when they're all happening together in one evening, it's pretty confusing. I've met the BDP type and clingy/stalking/harassing type before, and I don't think she's either. I quite like her, but:

Can anyone tell me what might be going on with her? Or, more importantly, am I/is she at risk of harm?

Thank you.