The last statement, yes. Miners receive less new Bitcoin for each block, which, of course, assuming the price stays the same, means that their mining becomes less profitable. The price itself isn't directly tied to the block reward, though the market has recently been more volatile in anticipation of the halving.
It's a little more nuanced than just getting paid half as much to mine. Miners earn income form two sources, a per-block "subsidy" (source of the mining analogy, this is simply materialized and given to the miner), and per-transaction "fee" for each transaction included in a blocks (these fees are paid by the transaction initiator). Only the subsidy is getting halved. I think the long term vision was the fees would be the main source of income, but they've never made it past around 30%, and are currently only about 5-10% of the total reward.
I don't think so, after all there was a soft-fork (SegWit) and a few hard-forks (Bitcoin Classic most famously) just to address the high volume of transactions. I think the creator did not anticipate bitcoins becoming so valuable. The high value means that people are only willing to pay small fractions of the block reward as fees, because that's worth a lot of money.
