Yes. There are no work restrictions on a UK Ancestry Visa. In-fact, the whole idea is what you're going over to work.
However, note that you are not covered by the healthcare system and have no recourse to public funds.
Your ancestry is irrelevent as are your European ties. If a visa is required for a country, all people from that country must get one. The UK consulate won't be taking a DNA test, nor will it ask about your ancestry. Currently no American needs a visa to visit the UK. If you plan on staying longer than the allowed visitor time or work in the UK then yes you need to apply for a visa.
You can establish your own business in the UK if you have the UK work visa.
No, you generally need a visa to work in the UK as a foreign national.
No, you generally need a visa to work in the UK if you are not a citizen or a resident with the right to work.
No, US citizens cannot work in the UK without a visa.
no
Yes. You can get USA and UK work visa without any sponsor or degree.
A work visa
If you get the UK work visa then the work permit is not given to US so you need a work permit for US.
Yes, a UK citizen can work in the US with the appropriate visa or work authorization.
The visa that is required for Pakistani people to do business in the UK is the UK Work Visa or UK Business Visa but it may be vary according to the category of your Business. For any type of visa Julia & Rana Solicitors in Pakistan provide best Visa services. You must consult with them before applying for any type of Visa.
You can get the five years work visa of UK and after five years of residency, you can acquire UK citizenship by naturalization after obtaining the ILR.