If I travel, will I face any problems when coming back to the UK? I am outside the UK -  will I be allowed to enter the UK? What are my rights to enter the UK? What documents will I need to show at the border?

The rules around the right to enter the UK are very complex and depend on many different pieces of legislation. Factors such as your nationality, whether you were living in the UK before 31st December 2020, whether you put in an application to the EU Settlement Scheme before the 30th June 2021 deadline or not, all play a part.

See https://www.the3million.org.uk/rights-enter-uk for a comprehensive description of your rights to enter the UK.