The halving will take its effect in the next few months or years. The price will rise due to the reduced supply.
The supply is not reduced. It increases toward 21 million with every block.
The daily supply of the new coins are reduced, or you can say the rate of the new bitcoin growth reduces.
I see that you have a full understanding, but "daily supply" is a poor term because the supply of bitcoins each day includes all bitcoins in existence, and not just the ones produced that day.
"Production" is a better term than "supply of the new coins" because it is more accurate and accepted, and it isn't as confusing.
That is right. When the bitcoin price rises, some holders will be attracted to sell their coins, that will increase the circulation.