When using investment firms such as Charles Schwab, can you invest your money in any individual stock?

I want to invest money in individual stocks instead of having to get plans such as 401K's.

You sure can. Open up a brokerage account and you can invest in stocks, etfs, mutual funds, CDs, bonds, options.
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Yes you can....

Also: Consider ROTH IRA's. Great tax advantages.

And: Whenever I left an employer I'd switch my 401K
funds to a Schwab Rollover IRA. So I'd accumulate and later be able to invest as I liked (+ great tax deferral).

Statisically it usually pays to use the 401K. More cash to invest & less taxes (+ sometimes an employer match).
So.... you can do as you asked... but look at it from all points of view.

Definitely. Schwab is a broker, and can handle your stock transactions. You can trade online with them if you want to, or call them and work with a person. If you have money in your account that isn't invested, it will earn interest in the meantime.

Well, almost any. There are some you will not be able to invest in. Those traded only on some foreign exchanges. But many foreign stocks are available on the pink sheets. You can invest in those. As for stocks traded in the U S and I think also on the Toronto exchange the answer is yes. Schwab may also allow trading in stocks on certain foreign exchanges. Etrade does.