Is there anyway to get rid of the "BLFK" or w/e that appears in certain unit's Status boxes?

You mean BLNK that appears in the wireframe?

Short of modding, no.

It's BLANK, they just removed the vowel, and no, there is no way, if you really don't like it, avoid using units that were only made for use in the Mission Briefings.

Aldaris was made only for the Mission Briefings?! What on earth. I remember killing him in one of the scenarios.

Haha, that was actually a Tassadar, they just renamed him, if you click him he has the portrait, and while there is a unit for Aldaris, it has a blank wireframe.

Wasn't Aldaris a scout? I MUST be mistaken...

Edit no that was Artanis.

Who was Aldaris? And also, how did the makers of Scmdraft create new units like Aldaris and the battlecruisers without modding? Why can't we do that now?

SI hasn't created a unit. Blizzard did.
But since they didn't need the unit ingame they didn't care to create all aspects of it. See it as a dummy unit that just was given enough properties that it is useable in the briefing.
SI simply unlocked the access to that unit.

Interesting, that makes sense.