Recommend A Good General Purpose App To Edit Video Files?

I recently obtained a number of large video files. They have several different file types (file extensions). Among those types are:

.AVI .MKV .MPG .MPE .MP4 .WMV

There are other types as well.I'd very much like to perform some simple editing on these files. The most common editing operation is to extract or "split" a large file into several smaller component files. In other words, each of thse large files contain several small files - all strung together.For example, there may be 4 or 5 video clips in each file. Instead of creating one file for each "clip", the person who created these files just concatenated them all together in one file.So, I'd like to "split" each of these clips out of the single file and create a number of separate files - one for each clip.In addition, I would very much like to be able to convert files of one type to another type.I don't know a lot about the attributes of the various file types. I've read about them in Wikipedia and so I know a lttle about the reasons these file types were created and what the various differences are among them. The main reason that I'd like to convert most of these files to a single file type is that I consider it kind of sloppy to leave these files in there original file types.I have used the app Irfanview in the past to perform similar conversions on "still" files such as .JPEG or .GIF files.

1) How easy or difficult is it to convert video files from one type to another?

2) Should I expect to find one app that can do both editing and conversions? Or should I expect to get several different apps - some to convert files and some to edit files?