Converting video clips already edited in timeline?

Question

Hey guys, excuse my noobiness, I am in fact one.
I recently have learned that before importing my footage from my canon g20 into FCPX it's best to convert the files to .mov. first of all, is that correct?
assuming it is i got the brorsoft video converter for mac which i havent used yet, but from what i gather it's pretty easy to import files from my camera into there, then export them as .mov files to make it easier for FCPX to work with them. Let me know if all that is correct.
Now, onto the main question. Before i learned to convert files upon import I already started a lengthy project in FCPX. It's full of very quick hard edits and cuts, as well as TONS of sped up shots. I haven't exported the project yet, but all the shot that were sped up to 4x or 8x playback very very choppy in FCPX.
My questions are, should i assume that the sped up shots are choppy because the files weren't converted before import?
Will it playback as it's supposed to after i export it? meaning is it only playing back choppy because i'm veiwing it in the timeline, and when exporting it will fully render to playback smoothly?
Lastly, if i need to, can i convert the edited files in my timeline? So, if the reason its not playing back smoothly is because the files weren't converted, can i do that now? even though the whole piece is edited and sync'd to music.
let me know, if you could help me out at all as, like i said, I'm very new to this. I also have 2 projects that I'm waiting to start until I can figure out the best way to get the best quality and best playback before starting them.
late '12 imac 27"
3.4 i7
32gb RAM
3tb fusion
680 2gb video card
THANK YOU

Answer 1

its rendering now, we'll see. I really appreciate your help Tom, thank you.
as i mentioned earlier, i got some software called "video converter" for mac by a company brorsoft. I can import whatever the file type is off the canon g20 (still unsure what file type it is exactly) and then export it as any file type i want.
Is there an ideal file type i should be using when importing to FCPX? prores? .mov? mp4? I have no clue what works best without sacrificing video quality.
and the original question was since i already imported video for a project, which i edited, fine tuned, and is complete just the way i want it, can i convert the clips that are already in the timeline without messing up all my edits, trasitions, etc..? do i even need to do that?
also, when i export the master file, does it somehow render the project even further to where it will look different than whats playing in my timeline now? when doing so, whats the highest resultion (what file type) i can do for a youtube upload?