I am an Indian staying in UK with a student dependent visa with full work permit. A US company want to hire me to work remotely in UK as Software Engineer. They don’t have operations in UK. Can they acquire me as a permanent employee in this case? What all are the options they have? Also to which country I should pay the tax?
In terms of hiring you it's up to their HR department to sort that out.
If you want to stay in the UK it will be up to you to update your visa or apply for a new one with the UK government. You can ask the potential employer for assistance with this but there may not be much they can do beyond provide proof of income for you since they're not in the UK themselves.
Generally you pay taxes to the country you reside in. In your case this is the UK. The US is a bit of an exception where its citizens must file taxes with them regardless of where they work or live, but since you aren't an American citizen that does not apply to you. File with the UK.