When using the "Import" functions, is it necessary that I check each mod that appears in the list to the right?
Also, is it safe to enable a mod that has been imported into the bashed patch?

First question: In most cases yes. That is how the most of the import tags actually get used. The only exceptions I know of are for FCOM (Factions and Relations for OOO, do not load)
Second question: It is safe, but unnecessary. Merging a patch into the bashed patch allows you to have it active, without actually being a part of your mods to load, thus allowing you to have more, non-patch mods active.- That is to say, it's technically already active as a part of the bashed patch, without actually being activated.

So imported content (the dot) is the same as a merged mod (the check mark)?

Thanks for clarifying.

No. Merged means totally, well, merged. Imported means that *some* stuff has been... yeah, imported. Sometimes, pretty much all that there is to import, can be, so it's rather similar to merging, in the end. But other times, not so much (in which case, you'd want to leave it activated). Wrye Bash itself (especially now) tells you a lot of this, or lets you know in one way or another at least. BOSS is also excellent for such details.

Thanks for the explanation. To be safe, I enabled all of the imported mods except for All Natural - Indoor Weather Filter For Mods.esp.