I'd like to base camp on Vern Lake (or Vern River if there are any spots) (or possibly Homer Lake). Can anyone tell me if there are any campsites on Vern River, Whack Lake, or which sites are nicest on Vern Lake or Homer Lake? Any favorite places in the area? I assume you cannot get from Vern to Weird Lake?

Click on the "Maps & Entry Points" tab at the top of this page, click "by Entry Point" on the drop-down menu, then click on Homer Lake. The map shows one campsite on Homer outside the BW, 1 inside the BW, 2 on Vern, 3 on Pipe, 3 on Juno. There is some information available on some of them by clicking the pop-up.

I went to Homer and Vern Lakes last year.
Both are nice lakes, I will definitely be returning. Campsite 962 on the east side of Vern Lake is spacious. The trail to the facility is long, I didn't mind that. My BIL and I tried to paddle to Weird Lake, but we didn't make it. The Vern River gets narrow, and we didn't want to chance it.

Be careful on the rocks in front of Campsite 962. My BIL's canoe overturned and mine just drifted away...you wouldn't have the troubles we have. Nobody does, really.

I see campsites referenced by number sometimes (like in this post) - and I'm unsure where people find that info. Does this site or other websites show all the BWCA camp sites, by number?

Yes, just follow the instructions I gave you in the above post to get to the map. The red dots are campsites. Left click on it with your mouse and a pop-up will appear that gives you the campsite number, as well as a rating, assuming someone has rated it. Below that it will say "View Camp Detail". Left click that and you'll get additional information.

On the map, you can zoom out by clicking the minus sign ("-") in the upper left corner of the map or zoom in with the plus sign. You can also scroll north-south or east-west on the maps by holding down the left button and moving your mouse up-down or left-right.

Spring Fever Again- 2: "I see campsites referenced by number sometimes (like in this post) - and I'm unsure where people find that info. Does this site or other websites show all the BWCA camp sites, by number?"

Boonie's right, I looked up the campsite number on this site. Also when you get your map of that area, each campsite is marked with a red dot. McKenzie Map Company makes a great map for Homer and Vern Lakes, its map #21. (it also includes Sawbill, Cherokee, Brule, etc).
If you email Sawbill Canoe Outfitters, info@sawbill.com Dan and Claire would probably send you their "Welcome to Wilderness" planning guide. It has a map that shows the area from Brule Lake to Lake Insula, including Homer and Vern Lakes.