So does mining account for a significant portion of the coins being sold? Is that why miners' decreased participation reduces supply?
Close to 90% of Bitcoin's have already been mined, so new rewards do not much increase the supply.
However, consider that mining accotns for all Bitcoins in circulation and it's hardwired so an increase in demand would not result in a change in supply. Trades are constantly being made on the different exchanges, halving introduces new coins into the Bitcoin market, when that reduces and demand increases, buying pressure increases.
Also who halves bitcoin? Like how does it halve?
The protocol was designed that way, every confirmed block comes with a coinbase reaward and every 210,000 blocks (~4 years) the reward halves. Same way difficulty is adjusted every 2,016 blocks (~14 days)
Full nodes verify all transactions and ensure its following the designed protocol, this is the consensus rule -
https://en.bitcoin.it/wiki/Consensus