Change of nationality and reapplying for H1 with expired unused visa period

[vars]

Hi

I was having 22 months of H1 visa in my indian passport left when i left US in 2010 , and my h1 visa got expired in 2012 ,

This year i am eligible to apply for UK citizenship and if my passport changes to british ,

1)Can i still claim my unused period of H1 after my changed nationality using previously approved I797

2) If i come to US to visit my immediate family , will it affect in any respect if i apply for H1 visa in the above process

3) how long am i eligible to use the unused period of my expired H1 visa ?

Please let me know

Thanks