BELT - No you do not need to remove the mount. you will notice there are 3 legs on that engine mount that is in the way. The lower leg needs to come off. Removing the whole mount is a pain and more work than needed.More on that in a second...
White smoke/wet plugs - Sounds like there is antifreeze getting into the combustion chambers. You may have bad head gaskets or possibly a cracked head or block. More on that in a sec...
How to replace the belt -
You will need a small flathead, either an E-12 or E14 external torx socket [I forget exactly, autozone has a set for $8 with 4 sizes], a ratchet, and a 15 mm socket or wrench, needle nose pliers. New belt, preferably gatorback.
1) turn wheels to extreme right or remove passenger front wheel.
2) Remove 2 tabs that hold the front lower fender cover. [needle pliers]
3) Make sure you have something showing the belt routing, don't assume you will remember how to re-route it. [owners manual may have a diagram, check it against your engine JUST to be sure it is identical Do not trust the diagrams on the belt packaging.]
4) Using the 15 mm, turn the belt tensioner to loosen the belt, and slip it off the tensioner.
5) Below the leg of the engine mount you must remove, there is the crank sensor. Disconnect the plug with flathead so it will not be in the way.
6) It is not necessary to remove the nut around the torx bolt. Remove this torx bolt [with the e12 or e14..]
7) Now the spacer must come out. Move it upward and work it out, it is a little stubborn.
Now remove the old belt.
9)Now would be a good time to make sure all the pulleys Except the crankshaft are spinning smooth and are not wobbily.
Installation is the reverse of removal, except these things -
Make VERY sure the belt is seated well on all pulleys. Now double check.
When working the engine mount leg spacer back in, it is even more stubborn. The side of it away from the engine, you may have to lightly tap it back in with an extension and a small hammer. Some folks recommend rounding the edges of the spacer.
It is more of a pain in the *** than complicated to do this job.
Gasket/crack block - To check the compression of the engine you will need a compression tester. They are not real expensive. They just screw into the spark plug holes. Look more for uniformity between cylinders than a specific psi. 5 cylinders with 120 psi and one cylinder with 50 psi means there is a problem. The results of this test are more accurate when the engine is warm.