The answer to both of these must be yes.
If they are independent, they will be unbiased towards any investment fund, bank or mortgage provider and only offer you solutions that meet your requirements and not theirs.
If they are regulated by the Financial Conduct Authority, you know that they have had to comply with rigorous guidelines and certifications for both individuals and their  business as well as undertaking to treat all customers fairly.  Further details of the FCA guidelines for financial advisers can be found here: Financial Advisers | FCA