Ask an Property Solicitor. Get an Answer ASAP.
First off, she has no right to "claim" your land, even if you have left it on the other side of your fence. This is a trespass and you can demand she removes her items from your land.
Secondly, she seems to be under the misapprehension that you are obliged to have the "ugly" side of the fence (ie the posts) on "your side". That isn't true - the posts can be on either side, although when ownership of a fence isn't known it is often assumed that the owner is the one with the posts on their side.
I recommend you write to her, warning her to remove the items from your land within 14 days or you will issue injunctive proceedings, to get a court order to remove the items and prevent future trespasses. Tell her you'll claim costs against her too. If she doesn't comply, all you can do is see through the threat - this might cost around £3000
Yes, absolutely. You can list your demands for the position to be restored and the trespasses to end.