I just want to know what 9 speed components I can use on 10 speed drivetrain. If I have 10 speed cassette and 10 speed shifter, can I use (1) 9 speed rear derailleur? (2) 9 speed front derailleur? (3) 9 speed crankset? (4) 9 speed chain?
Thanks!

You need a 10-speed chain for good shifting performance and less chainrub.

How about the other components? Can I use some 9 speed parts without sacrificing too much performance?

Yes, depending on what you call "too much".

One key thing is that the RD must be of the same generation, and brand as the lever, so the cable response ratio matches. Makers don't change this often, so it's a question of being of the right er, not the specific year.

Expect some marginal loss of shift response with a front derailleur whose cage is designed for a wider chain than you're using. Also, on some 9s cranks chainring separation can be enough for the narrower chain to hang between the tips of the inner ring and face of the outer on downshifts. (OTOH- you'll have problems with chain rub riding the inner ring with the outer cassette.

So it's doable, and folks do it all the time, but you need to be sharp about it.

Thanks for the explanation. A very simple example:
Can I use 9 speed rear MTB derailleur on 10 speed cassette?
Can I use 9 speed MTB crankset on a 10 speed drivedrain with 9 speed FD?

First question: Yes. You need 10-speed shifters but a 9-speed era rear derailleur is fine.
Second question: Yes on the crank, probably yes on the front derailleur. I've used a 9-speed Shimano crank on an otherwise 10-speed bike with no problems but I did have a 10-speed fd.

This is where the generational match question arises. I don't track specific models, but often the cable response ratio for mtn derailleurs is different than that of road derailleurs, so mixing platforms won't work. You need to check the specific compatibility before starting the project.

Likewise, some companies have slightly more chainring separation on mtn cranks than on road, since you're already using a narrower chain (10s vs 9s), more separation isn't good. OTOH it may work, just something to be attentive to.

The crankset chainring separation is also an issue for indexing FD levers, since the travel may be inadequate. Correcting for this is harder on a triple than a double, so it could be an issue.

This is beginning to sound like one of those "if you need to ask, it's beyond you" threads. Many of these mixed setups can be made workable, but many cannot. It goes down to the specifics, and even in the best of cases can be more demanding of mechanical skill. I can't help you more, and suggest you find a friend or bike co-op to advise on compatibility, and walk you through the trickier patches if you go ahead.

To the OP's original questions yes, yes and yes and #4 I don't know for sure but as Al1943 mentioned you may need the 10sp chain which is exactly what I've been running for a few thousand miles now. Ultegra 6500 crank and derailleurs with 6600 shifters and cassette + 10sp chain. Works flawlessly. Can't answer about the Mtn. components though.

Ignoring the pulleys and such, the actuation ratio for Shimano has been the same through many generations if you ignore DA oddballs. It has been the same since their earliest 1980's SIS to every RD up to 9 speed MTB and 10 speed road still in production. 10 speed MTB and 11 speed road are different. All microshift derailers are also the same.

Campagnolo has gone through 3 from what I understand. Original DT index, pre 2000 8/9 speed and post 2000 9/10 speed. I'm not 100% clear if the ratio has changed with the new 10/11 speed groupsets. Campagnolo claims incompatibility, but so does every other manufacturer that doesn't want you to mix and match.

Sram changes with every change in speed, I think.

Only issue is the chain. You need a 10-speed chain for a 10-speed cassette. Everything else the OP posted should work, although front shifting may not be optimal.

If you are thinking of using a mountain bike crankset on a road bike there are several possible problems although this has been down my many.

First of all, in many cases the front derailleur cannot be lowered enough to work acceptably with the mountain crankset. This is a common problem with braze-on style front derailleurs used as standard equipment on many modern frames, especially carbon fiber frames. This can also be a problem for a road crankset with small chainrings.

Many mountain type front derailleurs are top-pull which do not work with STI road bike shifters.

The front shifter cable pulls and actuation ratios are different from road bikes to mountain bikes.
As others have said, most rear mountain bike derailleurs are completely compatible with road shifters, including certain lower level 10-speed mountain bike RD's. Dyna-Sys rear mountain derailleurs have a different actuation ratio and are not compatible with road shifters.

Some 9-speed triple ring cranksets do not work well with a 10-speed chain if the ring to ring spacing is too wide. This falls into the "try it and see" category.