apnā = "one's own", and it must be used (instead of all the other forms) when the subject of the sentence is doing the possessing. "tum" is the subject of this sentence, so you can't say tumhaara, you must say apna. There's a logic to it, somewhere down the line... but just think of it as a wacky rule of the game.

"aap" is not related to "apne". That would be "aap" and "aapke". Aapne refers to the subject of the sentence, no matter who that subject is (I, he, they, whatever).

The sentences is tricky because the Hindi version has a postposition that is only implied. Look at the English; the phrase is "at this time." While the Hindi sentence has left out a word corresponding to "at," we still understand it to be there. And it being there puts the phrase "this-time" into the oblique case. (इस is the oblique case transformation of यह.)