Yes, yes, and yes. Caveat: mercalli 4 does not like it if you mix up the frame rate, so keep media, project settings, and rendered output at all the same frame rate. (Or render to an intermediate to 'lock in' the stabilization then re-import into project if you want to change the frame rate.)
Let's say your source is 50p, and want to put into 50i/25p project... so it means you should temporarily make new project, put the 50p on the new project, and apply Mercalli 4 stabilizer rather than apply directly on 50i/25p project?
Never used 50p, but I think it would have the same problem as others have seen if you try to stabilize it on a 25p timeline. So, yes (assuming I have understood correctly) put the 50p footage on a 50p timeline, apply stabilization, then render it out to intermediate format at 50p. Then place that on your 25p timeline. This is all to prevent mercalli getting the"jitters" and also because it sometimes continually asks for re-analysis.