How is software hacked and patched?

You can't. Anybody running anything locally has total control over what it does - if you phone home, that can be disabled, or intercepted. If you do key checks, they can be altered to accept any key. Hardware checks, and again, you can change that to always return true. No protection that runs entirely on an open, local computer will ever be 100% effective - the only method I've ever seen work is putting important logic on an external server somewhere, and verifying when that's asked for - but that adds latency, complexity, and annoyance.

Simply put, I wouldn't try too hard, it'll be cracked, and then the only thing it'll do is irritate legitimate customers. If your software is good, the people who matter will buy it, especially if it has any business applications.

There are just a few software protection products in the world, which are in use by all software makers. As such, they are well-known to hackers.

These protection products are faced with groups of young geniuses, groups that are being continuously renewed by newcomers. In addition, they are in competition with each other, racing forward to crack any new product or security schema. They keep count of their exploits using dedicated websites.

For these groups, cracking a new product is just a matter of finding out which protection it uses, then nullifying it. It is more interesting for them when a new version of the protection product comes out, cracking them usually within days (!).

Many legitimate owners of games/video/music prefer downloading cracked versions, since the protection products can be worse than viruses, causing big problems themselves after being installed.

In conclusion, using your own protection scheme is the best idea, rather than buying one, but knowing that if your product becomes well-known then it will be cracked.

You can't. Anyone can alter any blob of data on its own computer (that's a statement about possibility, not ability, legality or license).