Autistic neighbour (new neighbour)

She is an autistic person in new surroundings with new people.

Probably incredibly overestimated and overwhelmed.

You do not have to like each other. All you need is to be polite and have good boundaries. Simply leave conversations and situations that you aren't comfortable with.

Things may change in time

You don’t say whether she lives alone or with others? If there are others in the house perhaps you can have a word with them. Do you actually know she is diagnosed autistic or are you just taking her word for this? This is a complex situation with so many variables. It is difficult to see how to handle it .

Onwardandupward
Have you put personal stuff on FB?

I wouldn’t be too happy with that. Keep a polite distance!

Well, I saw her again and smiled and said hello as we came face to face (Im just not a rude person but sometimes I wish I was!)

It seems like she's really uncomfortable with new people, but it really disturbed me when she said things that proved that she had been researching me. She knows too much for someone I've never spent time with! Very strange experience She was actually trying to sound like she knows more about my life than I do...

backing away slowly!

Sounds as though she has announced she is Autistic and now feels she can behave as rudely as she wishes.

AVOID!

BlueBelle

If I was in your position I would just be smiley and friendly towards her without getting involved in conversation Just a hand up and a good morning etc and carry on your way
that way you are showing her you are a pleasant friendly person without needing to get involved or be in any way threatening

Sounds about the best thing to do.Does she live alone? If she needs anything she may come to talk to you in future.

I would just smile and say hello as you don't want to cause her to be fixated on you especially if she was a bit aggressive. Let her be if you can without feeling intimidated.

If I was in your position I would just be smiley and friendly towards her without getting involved in conversation Just a hand up and a good morning etc and carry on your way
that way you are showing her you are a pleasant friendly person without needing to get involved or be in any way threatening

As an equine therapist for many years, my wife worked with many autistic clients. If I understand her correctly, apparently autism is often only one among multiple mental challenges with which the individual struggles.

I would let it be until she approaches you. If she is aggressive I would tell her kindly but firmly that that is not how you live your life, and then ignore her. Make sure you do not spoil your own activities and become very aware of what she is doing, just carry on as before.

My experiences with people on the spectrum is that they are all so different. You’re already giving her some thought by trying a smile and a wave. If she appears unhappy with that, and is inclined to be combative, then ignoring her unless she specifically approaches you is probably better for both of you.
Things may settle down when she’s settled in-let’s hope they do.

Write her a nice straightforward note. Thank her for telling you she's autistic and ask her how she'd like you to interact with her most usefully.
The written word is consistent so she won't have to cope with your facial expression and tone of voice adding possibly confusing information.
Word it carefully and positively. It sounds like you're a friendly sort of person and keen to get on with others. Try not to use abstract or emotional words. Good luck.
Don't forget that there will be more to her than her autism. She may have unfortunate memories of a previous neighbour for example. It's likely that she'll be highly anxious too. A quite calm approach should help.

This individual sounds complex. Honestly, I’d avoid her.