How best work in US from UK as dual citizen

Hi I am considering working for a US company part-time while also working for a university in the UK as a dual citizen.

What things should I consider before pitching this idea to a US company?

Would I have to be a contractor? Do I have to set up own business to do this (e.g., sole trader) or can I be self- employed without setting up own business?

What kind of tax implications would this have?

What kind of salary range should I consider ( not sure what it would be like for US vs Uk for a PhD scientist with 7 years industry  NPD experience) .

Many thanks!

Our daughter is currently a full time employee working for a US employer while living in the UK. She is also a dual citizen. Her company says they are working on paying her out of their UK office but still have not got around to it after 7 months of her living here.  She has not had to set herself up as a contractor or sole trader, she will pay UK taxes based on her gross US salary, and those UK taxes become foreign tax credits when she files her US taxes. 

If your company is amenable to the idea it would be up to them I think as to whether they paid you as a contractor or not. You will be liable to both UK and US taxes based on your worldwide income.  With your UK university job you will be paying into the UK State pension system (National Insurance contributions) plus you will get whatever normal benefits a UK employee is entitled to.

I would recommend seeking better advice on the subject from a tax pro, but what you are suggesting is perfectly doable I think.