Question: Can I be the transaction processor and take in transaction fees as income without mining a Bitcoin? Would the fees be so low that it is not practical?

Or is it true that I have to be a miner in order to process any transaction? However, after year 2140, when all Bitcoins have been mined, then will people only use the computer to process transactions without doing any mining?

Answer: 
It's a combination of the low trade volume, and also because the traders on Bisq know that some people will pay a premium in order to avoid having to complete KYC requirements to do their trades.

If you signed up for an centralized exchange, you'll be able to buy at the market rate (minus a fee), but the trade-off is having to complete KYC requirements.
Post your own offer at a reasonable rate and wait. You'll likely pay less than fees you'd incur from coinbase or such.