I built quite a few houses in Texas on GUMBO soil which dries out so bad you need to water it to reduce chance of foundation cracking. You are correct in using a soaker hose to water the area around your slab. It also helps to remove 3' wide x 2' deep area around your slab and fill with gravel/sand ...

With your grey water line dumping straight out you dont need a trap or vent. You might consider a screen to keep the critters from coming up the pipe and stealing your soap.
Also consider a pea gravel trench to disapate water..after all you might not want an ice rink in winter

You might also take this oppurtunity to add rigid insulation to the roof deck before covering

another way to add insulation is with styrofoam sheathing (1/2" to 3" thick) The sheets can be added to the outside prior to residing and over the underbelly but you would have to add belly fabricl to keep out critters and bugs

The biggest heat/cool problem in a MH is that there is no return air ducting. All you get is under the doors and thru the face of the blower. If you could duct the vaulted part of your ceiling to the furnace chamber (filtered of coarse) you would solve heat build up in winter and summer

Call your electrician back...he screwed up

I am not so sure that gutters are a good thing. Without an overhang Im afraid of ice daming. What do you think?

Most of the new surge protectors have inlet and outlet for phone and cable connections

The trap does not have to be directly under the drain..you can 90 degree a fitting to a point that you could get to a servicable trap. I have installed many 4 piecers. With a good quality back caulk they work great. Try not to expose any caulking because that creates a re-caulk down the road. Defina...

It does not appear that your leak is from a blown off cap..that leak would show up inside the pipe. Check your roof flashing as it appears that is your leak. Be careful with your vent pipe and make sure it is double wall (one pipe inside another) because if it single wall you need to replace it or k...

How about making a sub-sub floor system..
add joist to the bottom of the joist and insulate so trap can hang lower??

Sounds like you have done all the basics so try these:
Check return air duct for leaks
How old is carpet (could be shedding) (like Oldphart said)
Is closet where funace is drawing air from attic?
And the obvious.....dust bunnies

If you installed skylite in LR with motor your problem would be solved letting out heat. Install solar screens on window and reduce UV by 75%, Remove screens in winter to obtain solar gain. If you buy a good skylite (Vellux) they have all controls and are Argon gas filled, insulated glass with Low E...

I have a concern about laying down a full glue product over a floating vinyl floor. Would you have to worry about buckeling as with wood underlayment ?

If the door had glass in it that might be where the sun shined causing a hot spot and drawing humidity