No you cannot move now.
You have to wait till decision unless you got alternative visa (vsitior, Holiday working etc ).
Regarding relationship you can provide following
1.Pictures
2.Fhone bills
3.Financial support(joint bank account, money transfer to support)
4.affidavit from your parents or freinds
5.affidavit from her parents or freinds
6.relationship history statement
7.any registration certificate(merriage/de fact to
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