The answer to all of these is that there were no laws restricting the movement education or employment based on race. ( there were restrictions on education based on religion -Catholics Jews and nonconformists were not accepted in english universities in 1800 but would have been by 1900. There were fewer restrictions in Scottish universities, but I interpret your question as directly excluding those.)

The black population of England was concentrated in the port cities, but by no means exclusively - there had been a fashion for black servants in the 18C and these were employed across the country. Gerzina suggests up to 3% of the population of London was black. Rodger in the Wooden World points out that a large proportion of Royal Navy officers and men were black and that many were discharged from ships in the UK.

Freedom from harassment and access to an education is much more determined by wealth than by colour in this period.

Poor Irish immigrants certainly faced harassment from those who believed they were responsible for driving down wages, or may become a burden on the local ratepayers, whereas wealthy travellers certainly did not.