What are the effects of salting a thin steak that's grilled on a pan? What are the effects of salting a thin (1/4" to 1/2") beef steak right before being seared on a pan, compared to not salting at all? 

(there are no other spices used, salt or nothing).

Does the exact method of preparation matter to the differences (e.g. searing almost-frozen steak vs. thawed out)?

Obviously, I'm interested in effects other than imparting salty flavor.
Related answer to the question Is it okay to salt beef before or while cooking it?

TL;DR: Salting the steak right before searing does not noticeable affect the tenderness.

Concerning the (semi-) frozen or thawed steak: Is it bad to cook frozen meat without waiting it to be unfrozen?

Since your mentioned steak is quite thin I don't think the semi-frozen steak goes "bad".