Drive shaft bearing...Yes, excess play like you describe is how I check.
Jack...I think I have a 8 ton. But length of size very important. I I think mine is called "low profile" I have one of these.
http://www.jettools.com/us/en/view-series/jhj-series-bottle-jacks/JHJBtlJack But don't recommend them or maybe I'm just behind on times. I carried the jack in M/H since we got it in 2009. Couple months ago I wanted to use the jack on my pick up, because I didn't feel like digging the jack out of my pick up. The jack didn't work. I took it back to where I buy all my tire stuff from including valve stem extensions and "gator" caps". A wholesale tire supply type place for tire shops, but he sells to public also. He laughed and should me a rubber plug where the jack oil goes. He filled it up with jack oil and it worked. But my point is, my old 3 ton bottle bottle jack maybe 20 years old still works great, but it has a threaded bolt where the jack oil goes. And I've never had a problem. I think newer jacks have been "cheaped" out with rubber plug. Sitting since 2009, I think the jack oil evaporated out? I think I have 10 ton jack stands. I know they are Harbor Freight. I use 3/4 inch socket with extension to remove lugs because the back tires my regular lug wrench wasn't long enough. Also have torque and air pressure spec's written done.
Jacks... I found out the hard way, when I bought a jack many years ago for different vehicle, I slid it under the frame after buying and thought great, that will do the job. Then couple years later I had a flat and then discovered my mistake. When a tire is flat, vehicle is much closer to the ground. My brand new jack was to tall and wouldn't fit under vehicle. That's why I said in above post, do a practice tire change before being stuck somewhere. I do carry some 2X4's to level M/H when camping and but also 2X4's would come in handy changing a tire.
Also recommend a complete fluid change on every fluid.
Also if your drawers have a cheap plastic thing that holds drawer slide, pick up a spare. One of ours broke and was a a big hassle. Couldn't find one stopping at RV places when traveling. Our is "question" mark shape. If you look at it the way a piece of wood would fit in...looks like a "question" mark at the end. OH, the things you learn when RVing:) Hopefully CA doesn't use them anymore. There are much better available today.
http://tweetys.com/jr-products-70715-drawer-slide-socket-set-question-mark-shape.aspx?gclid=CK336MXh8NECFQ9EfgoderULeQ
