Can I sponsor my dad with I-130 while my mom waits for EB-5 I-829 approval?

You can actually file for but they have to surrender the conditional green card before being eligible to immigrate again.

Yes, you can sponsor your father for I-130. However, there are additional points that you must consider. Pending I-829 means both your parents are conditional permanent residents. Their CPR status will continue to be extended until final adjudication on their I-829. An
I-130 sponsorship may be a good backup option in case you anticipate an adverse decision on the I-829. In that case, sponsoring both may be worth considering.

The I-829 is for the removal of conditions on a conditional green card. In other words, your dad already is a permanent resident with a conditional green card and both parents are waiting for the approval of the removal of conditions. You do not need to sponsor your dad with the I-130 unless there is some reason the I-829 will not be approved.

There is no bar on filing multiple petitions for qualified family members.

As a U.S. citizen 21 years of age or older, you can always file a petition for your dad. Whether it makes sense to do so is a strategy decision that you and your immigration attorney will need to make.

The answer to your question is "yes". However, he may not apply for adjustment of status in the U.S. (because a conditional permanent resident cannot adjust status). Rather, the I-130 should indicate that he will apply for a visa at a U.S. consulate or embassy abroad.

Yes, but your father is already a conditional resident, correct? Both can pend but if he wants to proceed through your case and is already a conditional resident, he will need to abandon the conditional residence.

Possible, but quite complicated. You really should consult with a very experienced immigration lawyer because doing this process is not simple.

If you were a US citizen and over 21 years old, you can file a visa petition for your parents to immigrate to the United States.