Yes that will come no matter how long the price would be at this time. There should be a recovery first with bitcoin and then it will come next for the altcoins.
Not necessarily. Then again, it depends a bit if you mean a recovery in fiat or more of a recovery against btc.
Remember the last big altcoin season occurred when btc hit a high then started collapsing. We here are just assuming BTC will hit 20K or higher again, but it may be a while (or never) for that to happen. Perhaps 13K was BTC's current bullrun high and the next couple of months will be a slow decline? If so, whales will need to look somewhere else to make money. That's where BTC dominance could decrease as whales start feeding in altcoin waters.
So nobody knows what way it'll go. It could be a 2-3 month altcoin season starting soon... or we wait until after the BTC halvening.