Is it possible that two apps, one created with the old version and one created with v2, could not "live" together without causing trouble ?

There is absolutly no problem it is the case in sandbox.
One sandbox for both versions, and even the datas are restored properly when you change version.


Well, it is better to have 2 differents instances of JDom (because of evolution and deprecateds)
Let say that if you run many components, keep only 1 main shared JDom root (can be placed in template, or in the main component)

So if you run 2 differents versions of components, prefer to separate JDom also (not share the files between them)

The other possible incompatibility is possible between jQuery and MooTools, if your previous component has not been generated for jQuery.