Is it common knowledge to my opponent where I have put my card? I mean he obviously sees if I have put it on top or on the bottom, but how about if I count the cards and put it as the 6th card. Does my opponent know that or can I count in secret?
I am going to broadly rule that you can't hide your deck while doing things with it.
I assume the situation is Swindler; I can e.g. put Province there to push the end of the game, take that, or a Curse that now will turn into Copper; but maybe I didn't draw the Province or whatever I wanted so I put a Copper 5th and hope you think it was a Province 6th and don't play Swindler, which might nuke a Duchy, which you might call me on so man why not put something 6th and be safe, but there's what's my hand, oh it was all Coppers and I'd rather risk the -3 VP than guarantee the -1 VP as it turns out this particular time.
In general I don't keep information private unless it's naturally private. I specify in the rulebooks; money and number of cards in hand (for whatever game) are public. People look it up, a rare actual use of rulebooks. It's the classic case of, you could just keep track; let's not add tracking that to the game.
In that spirit, you do not get to hide where the card goes, if they care, which they mostly shouldn't. Since you can't hide your deck, it would be possible to visually tell, and let's not make this a vision contest. If you just kind of randomly stick the card in there, that's also public, not the exact position but that you did it kind of randomly. If you are trying to make it look random while counting down 6 I will ban you from the tournaments I run (I do not run tournaments).