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Do the Imperials have the passenger ships to travel from one planet to another, or is it very dangerous because of enemy fleets and perils of the Warp and only military, Mechanicus and Inquisitorial forces use spaceships?

AFAIK, the only 'common' type of inter-stellar trip average Imperial citizens embark on would be upon a pilgrimage, and IIRC most imperial pilgrims give up everything they have to dedicate a swath of their life to visiting holy Imperial sites. In general, interstellar transport is too expensive, too risky, and discouraged strongly enough where most Imperial citizens never leave their home planet, never mind star system.

According to Rogue Trader interstellar travel, except for a pilgrimage, is discouraged for most imperial citizens. One of the reason for this is that an increased amount of passengers/passengerships
would put an aditional strain on the Imperial Navy's already stretched ressources.

The "Imperial Fleet" consists of 3 kinds of ships, technically the Imperial Navy oversees just about all space travel:
-The Imperial Navy (warships)
-The Merchant Fleet
-Civil Fleet (I assume this is what transports civilians)

Travel between worlds is not as common as it is in most sci-fi settings though. Given the perils of Warp travel, it's really not going to happen unless you a very good reason.

The best way to think of it is travel in 40k is like travel in the 1500's, long and very dangerous, so most people don't leave home unless they join the navy or some other kind of ships crew.