There are very few ways of becoming PM without also being an MP. The PM must be able to sit in the parliament, so he must either be an MP or a member of the Lords. In theory, the current PM or even the King could make him a Peer, and therefore a member of the Lords, but neither is likely :)
Farage can't realistically be PM in the current parliamentary session anyway. His party needs to win, or do very well in, the next general election instead. At a national level this election is purely symbolic and dictates whether Reform will have 7 or 8 seats out of the 650.
I suppose that in theory if Reform could form a government after the next election, but Farage still didn't get a seat, a party colleague could become PM and appoint him as a peer. There's a rich history of politicians losing elections and getting appointed this way instead, though as far as I know none of them subsequently became PM.
Do you mean "must be able to sit in Parliament"? The Lords and Commons are the two distinct chambers.
There have been non-MP (ie non-Commons) PMs.
The last time a PM wasn’t in the commons properly was 1902, although technically Douglas Holme became PM before getting a seat, however Parliament didn’t resume until after he became an MP
A Lord can’t address the commons, which was most recently an issue when ex PM David Cameron was made foreign secretary in the dying days of the last Tory governemt.