Yes, the brown stuff is OK......just not a whole lot of it. If you see a sudden increase or notice stinky ears, then it's time to be concerned. As far as ear cleaning, I clean the inside of the ear well as far down as I can get to, but I don't spend a lot of time trying to get way down into the base of the ear. I'd rather my puppy be comfortable with me fooling with his ears than be squeaky clean. But check him out each time you post--you don't want to see redness, irritation or a lot of goop.
It is a good idea to use some cotton on the tip of the backer rod to cushion it. That should keep his ear from getting too irritated from the non-absorbent tip of the post. But taped in well, the post should pretty much go with the ear as it moves and not be loose enough to do any major rubbing.
Back tape the post all the way down to the end (that goes in the ear)--don't leave the backing rod exposed--it's closed cell foam and if you don't get it all the way down in the ear it will wiggle--feel weird to the puppy and he'll do more head shaking--also closed cell foam can irritate the ear--add a little cotton pad to absorb some of the waxy goop that always forms and to protect the bare skin from bare foam.
You're doing fine, everyone has problems with posts popping out when they first start posting. You are doing it right--take the whole thing down when that happens and start over--it popped out because it wasn't all the way in or not taped quite right. Stuffing it back down and putting more tape on never works.