...The way my AVCHD videos are saved/backed up from my camcorder are in a folder with 2 files, one .modd and one .mts2 per video clip. Would this still be ok to import?
In Finder if you looked at the camcorder memory card, you'd normally see a single file named "AVCHD". Inside that are usually a bunch of subfolders. Inside one of the subfolders are usually a bunch of .MTS files. I don't know the specifics of your particular camcorder.
You can usually download them from the camera one of several ways:
(1) Plug in camcorder via USB, mount it as a drive and copy the AVCHD "bundle" off with Finder. Then you import clips from that from within iMovie.
(2) Plug in camcorder via USB and use Sony-specific import utility. What that utility does in terms of file disposition, I don't know. How those are imported into iMovie would depend on the file format.
(3) Plug in camcorder via USB and import directly using iMovie. I've never tried that since I use FCP X, but most editors allow that.
(4) Eject the camera SD card or memory stick, plug that into the Mac and copy the AVCHD bundle over, then import into iMovie.
For any of the above steps that result in the AVCHD bundle on your Mac you can optionally convert that to .mov or .mp4 files using ClipWrap or ReWrapAVCHD. Why would you do that? Because it allows easier browsing from Finder. The opposing technique is just import to iMovie from AVCHD, don't bother converting and don't browse from the Finder level.
...I don't recall messing around with the files separately and this is the way they were imported from my camcorder.
Import utilities normally don't do that, but maybe this one does. See this excellent instructional video for background:
https://www.youtube.com/watch?v=WpBjGUlBTHU
...Would you happen to know if importing imovies (home video clips) to a thumb drive and plugging it into the USB on my Blueray would work?
That will often work but you'll have to check your Blu-Ray manual for what video file formats are compatible.
If your Blu-Ray player is internet connected and can browse a URL, you can upload the video to Youtube and point the player at that URL. The advantage is family & friends you give the unlisted URL to could also see it. However most Blu-Ray players and "Smart" TVs have truly awful internet browsing. That's one reason people get set-top boxes like AppleTV and Roku.
Whether you put the file on a USB stick or get stream it via AppleTV or your player, the quality will be vastly higher than burning a DVD.
Here's are two good video showing how to manage files and trim clips with iMovie:
8 ways to trim clips in iMovie:
MacMost 8 Ways To Trim Video In iMovie
Managing libraries and files in iMovie:
MacMost Managing iMovie Libraries and Files
More iMovie instructional videos:
MacMost iMovie