I've been playing using COV and better Bodies for years, and I never get those errors. The only error I get is the one caused by Better Bodies "One or more plugins could not fine the master files they depend on."
The "Not Able to Fine Body Part....." errors are very common for any BB mods. Mostly with foot and knees.
The BC Patch does remove them from your Warning.txt so that you won't see them, so maybe you use that. But the patch is not recommended, as it makes all the in-game shoes look like crap.
Your "One or more plugins" error is also harmless, but I'm sure you know how to correct it. Just update the Masters with Wrye Mash.
I dunno, removing objects from the .esp sounds suspiciously like deleting them to me, because that's exactly what I meant by delete.
Deleting files, as t0nemgub specifically asked about, means you remove the file from it's place in the Data Files folder. This could cause problems if the esp is looking for the file for other objects.
Removing an Object from an esp just means that you delete all the references of that specific Object (a piece of clothing in this case) from the esp. Which shouldn't cause any problems unless it's used in a script or Leveled List.
These two forms of "removing" are very different indeed.