Urgent immigration advice about making an application

Hi,
I would like to get an immigration advice about making an application to the Home Office, UK.
I came here with spouse visa but my marriage has broken down within the probation pariod. I applied for a contact order with my daughter and the court passed the contact order last week. I have only three weeks left before my visa runs out. I need urgent help of these questions-

Can i apply to the Home office now with the contact order for further extension of stay although the contact did not start yet?

Do i need court permission before sending the order to the Home Office?
If i am to take court permission i have to make another application which will take few weeks but by this time my visa will run out. What can i do in this situation?

I am working for royal mail. they have issued a letter about my visa stating that i must have to produce proof of my application/acknowledgement letter from home office before my visa runs out. If not they will terminate my contract. I need suggestion about this as well.
Please reply ASAP.
with thanks
Jabs