1) FCP accepts a heck of a lot more than .mov files. Sometimes, codecs do not play well with the the .avi container. In which case, go ahead and use MPEGStreamClip or SimpleMovieX to move your file into the .mov container. This is assuming, of course, you are using a codec that is useable in the mac environment (as opposed to, as an example, lagarith, which doesn't). If you are not getting a compression error (codec/container mismatch) please tell me what codec and container you are trying to import, and what the error is.
2) Again, .mov is a container, not a condec. Codecs determine compression rates which determine size. What do you mean by "big?" I regularly work with clips in excess of two or three gigabytes, and that is compressed. If I were to work entirely in uncompressed, they would be even larger.