Thanks for confirming. In accordance with your numbering:
1. As the property is in joint names you both have a legal interest and therefore a right to occupy. She will therefore be able to remain in the property indefinitely and until the property is sold or a court order.
2.You do not lose any rights to the equity and remain entitled to the share as held on title.
3. You will remain jointly and separately liable for the mortgage and at the end of the mortgage you should be entering into a new one or deciding whether to sell it.
4. There are no rules on having a mortgage if you do not live there any more. So long as it is not being rented out you would be entitled to apply for another mortgage.
5. So long as your name remains on the title and there are no court orders excluding you from the property you are entitled to return and live there legally. Practically is a different question and usually once a person has moved out it is harder to move back in, but this will not impact your legal rights.
6. A separation will be ideal as it would clearly demonstrate what both your intentions are.
7. This can also be included in the separation agreement, and if it is not kept to you would be entitled to apply to your county court to force a sale.
8. If you have a legal interest in it and continue maintaining it there is nothing stopping you receiving income from this.
9. Unless agreed, there is no legal obligation to maintain and it is usual for the person enjoying the use of the property to maintain it.
10. It is usual for the non-resident parent/main carer to be liable for child maintenance which is based on your gross income and how many nights, on average, they stay over with you each week and it can be agreed in a separation agreement between you.
I hope this assists you. If you found this information helpful please provide a positive rating using the stars at the top of this page. I will not be credited for your question without a positive rating. Thank you