It should come as no surprise that I have opinions.
1a. Sure, I don't see why not. It could add another layer of strategy, and such mechanics could be added to existing cards that don't fare well in the Hidden environment. A card like Sphinx isn't desirable in a Hidden game, but if it had an "if revealed" property by which it would grant the player 100% rather than the usual 50% cost of the discarded card, players might be more willing to use it in Hidden matches, even while still selecting an opponent's card blindly. (Maybe "if revealed" and target card is hidden. Also, revealing it yourself might be unfair. But I digress...)
1b. Yes. Being able to look at your hand, see which cards your opponent can see and which ones he cannot, and determining from that what he might see as a threat or be prepared for is a level of strategy that truly appeals to me. Looking at what's been proposed so far, it seems we'll be more likely to have mass reveals or selected reveals anyway. The only case where I'd think it needn't be disclosed is the self-inflicted reveal, but for uniformity, everyone should be able to see what is revealed.
2. The way I see it, if someone reveals a card or an entire hand, he's going to screen-capture it or write it down and keep careful record of the changes made afterward. This being the case, the cards may as well be revealed until used. Of course, playing Renewal would then undo the reveal as it's a discard and redraw, but that's fine. (It'll be visible in the discard pile and likely to be played next anyway.) If people want a temporary reveal, I'd think a card that "shuffles" the opponent's hand would suffice, allowing the player to examine the discard pile to see what cards are in the hand, leaving their actual positions unknown.
3. This is a tough one. If it's one card, ideally it should apply only to the next one drawn so the opponent's never seen it and the player didn't single it out to be hidden, and then the effect may as well remain until the card is removed from hand or renewed. In the case of hiding a card or cards that were already revealed, this is going to encourage people taking screen-caps before logging out or hitting back on their browsers to see what was hidden. The hide-and-shuffle idea I proposed in #2 could be employed here to hide the location of a card the opponent is likely to discard, and in such a case, I don't know whether it would be preferable to have the effect be lasting or ephemeral.
In short, such a mechanic would be useless except in certain situations, and it would encourage tedious record-keeping that might be viewed by some as cheating.