If someone is out of status and not allowed to work, but they work and cash their check, can they get in trouble for cashing their check?

If you're cashing it with legit ID (and assuming it's in your real name), you shouldn't. Don't let anyone try to tell you otherwise.

If they have a tax ID and want to file taxes, will that get them in trouble?

Nope. The IRS isn't ICE nor does it cooperate with ICE.

If they don't file taxes will that get them in trouble?

Yes. If you have taxable income and exceed a certain amount (personal exemption and standard deduction), you have a tax liability. To not pay that tax liability amounts to tax evasion and that's a felony.