Am I able to work in England as a Luxembourg Citizen?

No, not without a work visa........ for that you would require a high level degree in a STEM, years of work experience, a UK registered employer who is offering you a job and prepared to sponsor the work visa

Nope - since Brexit came into force in January, EU citizens need a visa to live and work in the UK

Only if you find an Employer willing to get you a work visa and sponsor you. days are gone when anyone can turn up and work here.

Yes, but as of 1st January 2021 you need to have a visa. 

Your Luxembourg citizenship gives you no more advantage than your US citizenship, unless you have acquired “settled status” from previous periods working in the UK as a citizen of an EU member state (i.e. Luxembourg).

I think you mean that you have Luxembourgish nationality.  The fact that you are also a US citizen is irrelevant, don't bring it up, they will not like it.  You can use your EU member country passport to work anywhere in the EU.  Although the national language is Luxembourgish, they generally use French for legal work and German for commerce.  England is part of the UK and not part of the EU.

Not any more.  Remember Bexit?

you are probably white, am I right?
If you are you can't work in England