when your contract runs out neither you or she are under an obligation to renew it, so yes, you already live their but you only have a right to while the contract says you can.
She will need to give you notice that she dosent intend to renew - what does it say in the contract about notice?
Do you get on with your mum? It sounds a bit strange that she would trade the security of a regular tennant, considering she could ask you to move out and then not get it re-let.
I think if she is starting afresh with a new contract etc then she can charge what she likes, although it is of course up to you whether you want to pay it or look for somewhere else