POE for first time H1b

Got my h1b approved in feb and I am planning to go in july. Will I face any issues at POE due to gap of 5months?
Also can I go to another state where my family is rather than job location?

No issues. Once visa is stamped you may travel to the US and join the H1B employer any time as far as the H1B job exists at the time of entering.
You can request your employer to provide you with an appointment or job offer letter with a start date around the time you enter the US however it is not a requirement.

Yes this is fine as far as your final destination is your work location.