99 tahoe Problems!

I have 132K miles on my tahoe. I get a crazy vibration in the suspension and sterring wheel at almost any speed when i hit a rough spot in the road, or brake. It does nto always occur when braking. I also have new brakes. Doubt it is rotors. Pitenger arms?
Also, i tow a 7X14 enclosed cargo trailer. I keep all my tools in it. While pushing up a hill it kicked into a lower gear and reved high for a long time. THe check engine light started flashing until after i slowed. I already had it pop up earlier saying a misfire in cylinder 4. I changed all the plugs and it went away. Now it is back. Same code. One mech says it is the intake manifold gasket? Any ideas. Light went off for a while, and then came back again one day when pushing it hard without the trailer.
I already have a fairly new (10K miles) rebuilt tranny. What else can i do to give it more towing power? The trailer is like 2Klbs empty. Probably 35 hundred w tools and sometimes upto 7Klbs with materials (wood, tile, etc.)
Finally, how can i improve my ever reducing gas mileage? I was getting 25o miles per tank and putting 22 gallons at a time in it. Now with the trailer i am getting less than 200!!! I drive 700 miles a week. I need better mileage!
HELP!

The vibration sounds like a loose steering part. Check tie rods, pitman, iddler, shocks and springs.
The miss could be cap, rotor,wires, plugs, injectors, manifold leak, bad cam lobes, the list goes on.
All of this could be your gas mileage problem.

Damn, that narrow it down! I already did the cap, rotor, plugs and wires. Have yet to play with the injectors or cam lobes. One mech said i had suck the intake manifold gasket. I just want to be precise if i will spend 10 hours fixing it.
Ive read a few people on here who had to replace sterring sensors and that made it better. Is that applicable?
Thanks.

check your universal joints.

The steering sensor is not a vibration it's is more of a slipping feeling.

I just recently replaced an intake manifold gasket, super expensive, but I took it to the dealership. Besides the leak, I noticed when ever I changed gears, reverse to drive, it rev from 1000 RPM's to abotu 2500 RPM's. Since changing the new gasket and other work, hasn't happened.

I've also installed Rancho shocks on my truck, I've never towed, but I have loaded up the cargo area with cinder blocks and it helped with the sagging. The brocher of the shocks says Rancho are idle for towing, it eliminates the sag when towing.

For better gas millage and help with towing... try installing new software. I installed Hypertech software and my truck drives like dream. I'm getting about 14 mpg. About 250 out of 3/4 of tank. Don't let it run below a 1/4.