Upvote:2
I'm fairly sure your leg between Stockholm and London Heathrow won't actually be operated by Cathay Pacific, but will instead be a CX flight number on a BA (British Airways) flight. However, that won't make much difference, other than meaning that whatever happens you'll have to change terminals (BA from Stockholm arrives into Terminal 5, Cathay use Terminal 3)
Tackling your questions in turn:
If you want, since it's all one ticket, they will happily check your bags through as far as Hong Kong. They should be fine to also tag some bags to HKG, and short check one only to Heathrow, so you can take things out during your layover
See #1. It's up to you. If you ask them to check it all through, it'll all go through. If you ask them to short check one or more bags, then you'll have to collect those ones and re-check them later
If you want to leave the airside of Heathrow, then yes, you will have to pass immigration to enter the country. Nothing special here with Heathrow, as a general rule to exit the airside of an airport means passing through immigration
Immigration is for entering a country, so there's no Immigration when you leave! Some countries have exit checks, but the UK does not
To be on the safe side, plan to arrive at Terminal 3 around 2 hours before departure, especially if you want to drop some bags off that you've used during your layover. Heathrow Security is often annoyingly bad (in most senses), but if you allow 2 hours then you've time for delays with getting to the airport, getting through security, finding the gate etc