What's involved in installing these conversion bushes?
You'll need to remove the standard bushes from the S14/S15 subframe that you're installing. There's a few ways to remove the standard bushes which option you choose is up to you (google is your friend). Once you've got the standard bushes removed you need to press fit the new bushes in their place. TIP: put the bushes in the freezer for a few hours before installing them. This will shrink them slightly to make things a little easier.
What's the advantage of installing an S14/S15 subframe?
The S14/S15 subframe has better geometry than the S13 unit and also offers more track (ie. width).
What’s the advantage of these bushes?
Besides allowing you to install an S14/S15 rear subframe in your S13, the solid bushes offer a more solid rear end = better driver control and feel.
Do these cause much vibration/noise in the cabin?
Not really. Obviously anything solid or more rigid is going to cause an increase in noise and vibration however I'd hardly say that it's noticeable. Chances are if you're installing these you've already got coilovers, your car is lowered, you've got an aftermarket exhaust etc. etc.
Do these bushes change the height of the subframe?
Yes, they raise the subframe which improves the center of gravity (roll center).