How can I apply for an EB-5 visa and EB-3 visa at the same time?

You can have multiple immigrant processes going at the same time. You should withdraw one once the other is approved, however.

Your I-485 Application based upon the approval of an I-526 petition will be approved in a matter of a few months. The EB-3 process will definitely take longer than the adjudication time if the I-485.

Yes, the fact that you have had an approved EB-5 petition on Form I-526 does not prevent you from qualifying independently on an alternative basis. There is nothing to prevent you from having an employer file an immigrant visa petition under the EB-3 classification once you have obtained Permanent Employment Certification. You do not have to withdraw either petition and you would want to file your Application for Adjustment of Status based upon the approved petition when a visa number is available to you under the quota. Theoretically, if you have your EB-5 Petition on Form I-526 approved but your Petition to Remove Conditions is denied, you could still utilize your approved EB-3 petition. However, you should note that, currently, the CIS is approving approximately 99% of all petitions to remove conditions filed on Forum I-829. Under very limited circumstances could you go back to H-1B status assuming you have not used up your full 6 years of H-1B time and several other factors.

You may have both cases pending simultaneously but, when they get ready to approve one of them, they will ask you to choose and withdraw one. If the one you choose is later denied, it does not preclude going back to the other one depending on how far along it is at the time of your choice. If you have been on an H-1B within the last six years then you do not need to go through the lottery again.

If you have an employer who wants to sponsor you and go through the admittedly time-consuming PERM process and expense, you could do the EB-3 process up to petition I-140, which is an immigrant petition based on employment. As this does not expire, I suppose you could use this to file I-485 if your I-829 fails, if your visa number is current and if the sponsoring employer is still willing to employ you after 4+ years. However, EB-3 must be a bona fide job offer in which you are expected to work with that employer on a full-time, permanent basis upon receiving the green card through that sponsorship. Asking the employer to wait that long may be stretching it. Given how this administration is viewing H-1B and L visa categories, it is difficult to say whether or not you could get another H1B. Whether or not you could be Cap-exempt is based on whether or not you used the full 6-year term first time around. If you did not, then you could file the cap-exempt application to capture the remaining portion. If you used all 6 years, then you must go through the lottery again.

At the second stage (after I-526 is approved for EB-5 or after I-140 Petition is approved for EB-3), when you are ready to file for adjustment of status (in the United States) or Immigrant visa process (if consular processing), you need to choose between processing through EB-5 or EB-3.

There is no prohibition on applying for EB-5 and EB-3. If the I-829 runs into trouble, you can apply for an EB-3 green card. You do not want to file two I-485s, so it is best to file the first. Once you have been counted in the H-1B cap, you can always fall back on an H if your EB-3 application is backlogged.

Yes, you are also permitted to file for an EB-3. You need not withdraw it, as you can always use it to immigrate later if you cannot remove conditions from your status and abandon your conditional residency.