I don’t know the answer for the first question but I suspect it may depend on the plugin.
For the second question, the Plugin Manager will show you the VST SDK version of the plugin.
VST 2/3 are different addons, so on the computer with only VST 2 plugins the VST 3 versions used in the projects won’t be found. Should be easy to install the VST 3 versions there as well.
Answer to question one: used vst and vst3 need to be the same on both computers. So if you USE a version of a vst3 plugg it cannot be replaced by a vst on the other computer and vice versa. But it does not stop there. For most pluggs the pluggs on the receiving computer need to be on the same or higher release version of the plugg. One way to get around the problem is to render to audio all tracks both with and without pluggs and supply that together with the project.
Answer to question 2. When you load a plugg or instrument for that matter, in the drop down list where you choose plugg/instruments vst3 will have 3 graphical slashes behind their name.
If you don’t want to have to deal with potentially picking the wrong one, you can hide your VST 2 plugins in the plug in manager. I’ve done that with duplicate plugins.