If I use the "Redeem on Steam" function on Humble Bundle and get the key, can I give that key to a friend in a mean of gifting it to him?
Yes, you can, but you shouldn't.
If you click "Redeem on Steam", you already have seen the key. There is no way to tell whether you have already redeemed the key for yourself or not.
Humble Bundle often offers the possibility to gift individual keys, which generates a URL that you can then send. This way, the key wasn't seen by anyone, yet. (Because it wasn't even generated.)
I can see only two reasons to press "Redeem" and send the key directly:
You already (accidentally) clicked "Redeem", maybe because you forgot you already had the game.
There is a time limit on keys, something like "Has to be redeemed before ..."
Humble Bundle has changed their policy on giving away individual keys several times in the past, so they might do so again in the future. There was a time when "Redeem" wouldn't show you the keys, but redeem them directly to your linked Steam account (source 1, source 2).
Strictly speaking, yes.
That Steam key is simply a key that unlocks a product on Steam. There are no restrictions on you sending this key to someone else to unlock.
Likewise, if you gave someone access to your Humble Bundle account and they activated all your keys, well, they just stole all your games.