Will logged hours move with my issue if I move it from one project to another

[noamdah]

Yes

[Nic Brough -Adaptavist-]

That's a good, detailed and clear answer.

All I'd add is that I suspect there may be some follow-ups on other issue data, so to pre-answer those...  Move tries to take everything, changing only the issue key and the "updated" date/time.  If you have custom fields that are project specific though, you may find you lose them (if the field exists in the source project but not the target), and you may need to add data for fields too (if the field is mandatory in the target, but optional or non-existant in the source)