Capitalism is private control over the factors of production. So you can for example have a socialist society in which the factors of production are owned by the community, but there's still markets and commerce.

To answer your rhetorical question, a lot of people think Capitalism stands for the corrupt ignoble western governments, unlike their own glorious reputable eastern "socialist" governments. /ironic

That has been gone over by Marx over 150 years ago. I'm not going to go over everything Marx said about capitalism, he wrote an entire book called Das Kapital about it. Here's a summary that does a pretty good job at getting Marx's ideas across. You can skip the first 2-3 chapters as the main criticism of capitalism starts around chapter 4. But some things refer back to the previous chapters so you might want to watch them if some parts of Marx's ideas aren't very clear.

As for you points, I'll do a short summary:

• Production of commodities and services is not capitalistic, we've been producing commodities and services for more than a millennia before capitalism was even a concept.
• Profit-motive is a poorly defined concept if we want to divorce it from capitalism. Profit-motive in the sense that I want to make all the money is capitalistic. But if we talk about the "profit-motive" in the sense that I want money so I could buy things I want to use, Marx argues that is not capital and not capitalism.
• Marx has a very specific definition of capital where capital is something that exists for the purpose of making more capital. If you make $10 mil and you buy a fancy house, that $10 mil you got is not capital and the house you bought is also not is not capital, but if you take that $10 mil and you for instance invest it with the purpose of getting $20 mil later, now it's capital. The capitalist definition of capital doesn't acknowledge the purpose money or things, so everything is capital which also makes it impossible to separate capital accumulation from just owning things you need to live your life. Your house is not capital, your car is not capital, your phone is not capital, the money you're saving up for a trip to the Bahamas is not capital. But if you own a company and the means of production within that company and you're buying in labor to use your means of production so you could siphon surplus value from the laborers work, that's capital.

The things you've brought up aren't necessarily the basis of capitalism. They're the basis of capitalism only if you want them to be the basis of capitalism.