To your first question: yes, that is exactly what they're doing.

To your second: there is a fee associated with every transaction. You can set the fee to something incredibly small (like 0.00001 cent), but miners will take the higher-fee transactions first, so you'll be waiting a long time.

So even after the block reward drops to zero, theoretically miners will still have an incentive to keep processing transactions.

I would imagine that at some point, maybe in 100 years, mining may not reward you more than the cost of electricity to mine. Miners won't bother continue--how will bitcoins continue to be hashed? thanks apeace!

The invisible hand of the market. In 100 years, if bitcoin transactions are still of value, then miners and people making transactions will come to an agreed upon transaction fee that will be suitable for both parties. And If miners drop out, transaction fees will go up.

Transaction fees will keep increasing (because of demand) and we would have moved to renewable electricity by then (free electricity), therefore miners continuing mining.

That's my opinion.