sorry for the delay on this, I assume you have figured it out by now but for anyone that comes along later:
Yes, the Coleman UT400 is the same as the Hisun HS400. Same for the various other sizes, all Coleman UTVs are rebadged models made by Hisun. The service manuals leave a lot to be desired, and leave out some important steps, but if you have some mechanical experience you should be able to figure out the missing parts.
No worries, i'm not sitting around waiting. I just enjoy solving mechanical puzzles.
F4 should be a 15 amp fuse and runs the fuel pump relay & dc jack. Without that you wont get fuel to start the engine. Replace that and see what happens.
When you turn the key to on (not start) you should hear the fuel pump kick on (slight hum under the passenger seat) for about 5 seconds before it builds pressure.
The little black boxes are relays, shouldnt need to touch those, and i'm not aware of any replacements aside from getting a new fuse box ($80ish bucks)