Applying for a postdoctoral fellowship in the UK, how can I find a host institution It's been hard to find postdoc and I found a postdoctoral fellowship (in the UK) that I want to apply to. Since I do not live in the UK, it is required to find a host intuition within the UK that should agree by sending a formal approval.
Research Fellowships must be held at a UK higher education institution/university in a  department that can show it is capable of fully supporting the research project and researcher. It is the responsibility of the applicant to contact the host institution and gain the formal approval from the relevant head of department or school before submitting an application.
I am not sure where to go from here, should I reach out to professors (as potential PIs)? or I should email the HR of universities and get more information?
If I get the fellowship, will I be the PI of the project or I will have supervisor?
In general, you should reach out to the person you'd like to collaborate with and go from there. Email professors you're interested in - they can help deal with the bureaucracy of their institution (approval to host etc). Bear in mind that some universities set stringent internal deadlines on applying to certain fellowship schemes.
Whether you'll be PI depends on the individual grant scheme. You'll have a line manager (most likely the professor you apply with) but not necessarily a supervisor-supervisee relationship.