The sway bar bushings that mount the bar to the subframe are split from the factory, you don't have to cut them. There are revised bushings now from your dealer that have a wear sleeve on them. Too early to tell yet how long these will last-they've only been out for a few weeks. There are not any instructions in the book to replace the links. You'll know exaclty what to do when you get the wheels off. There is one nut at the top of the link to the strut, and one nut on the link at the bottom where it attaches to the sway bar.
To remove the link you remove the 18mm nut from the strut end of the link, remove the 18mm nut from the sway bar end, and remove the link. To replace the sway bar bushings you remove the nuts holding the bar clamps, and remove the bushings. Here is a picture of them.
A leaking intake gasket will not make a noise. It will be a vacuum leak and cause the idle to be high, but the gasket is a steel shim, and does not leak. The noise you hear sounds like it may be the alternator. It may also make some noise when you shut the engine off as it spins down. You can remove the belt and run the engine for a minute to see if the noise stops. If it does, spin all the accesories by hand and feel/listen for anything out of the ordinary.
Yes, you will need to put the van on jack stands and pull the wheels to get to the links.
You are pushing on the top of the plenum to stop the noise? That is pretty strange. Some of the older vans had a plastic cover over the top of the plenum that said 3.3 on it, yhou may be able to remove this cover and look around. It doesn't sound like a noise that would hurt anything though.
If you buy a key fob an ebay make sure you get the right part number. the number is XXXXX the back of the fob, if you don't get the same number it can't be programmed to the van. A dealer normally will charge about $20 tpo program a new fob.
I can't say for sure on the LXI part, but I believe an LXI has the 3.8, and you can't get the 3.3. I'm not 100% on that though. I think you would also have power rear wing windows. You can take your vin number to your dealer and they will tell you exactly what you have.
The cups that the ball joints go into are part of the link itself. I enclosed a picture of the link, and drew arrows to the area where the joint is. Sorry if the picture is small, but you'll get the idea.