Can you file self-employment taxes and Retirement taxes later after filing your wage taxes? ?

I would advise you think about what you are asking.  Restating your question, you are asking if you can (1) intentionally under report income on your tax return, (2) sign that return under penalty of perjury that the return is correct and complete, (3) file that return in order to receive a tax refund to which you are not legally entitled.  

There aren't separate "wage taxes" and "self-employment taxes" and "retirement taxes." There is income tax. On your entire income.

(actually, some of your phrases would be appropriate for social security tax, but that's not one you file)

If you file an income tax return showing only part of your income in order to get a larger refund, you will be unable to file a second income tax return. You will have to amend the original. Which you cannot do electronically.

When the result shows that you got too much refund, you will have to pay back the excess before April 15. If you miss that deadline, you will owe penalties and interest.

No you can't. Period. You have to file EVERYTHING on one return--you can't split it up and file part of it one way and part another way just to get a refund. That's not how this works. Once you file your return, you will be subject to the IRS review of your status and wages--no matter what--and anything you didn't report correctly will mean you don't get ANYTHING until you file it correctly. 

1.  it's illegal.  2.  you'll have to pay the extra back.

There is a deferral of Social Security taxes available for the self-employed. Read the instructions for Form SE, Part III.  There also may be another credit you may be eligible for.  You must file all your income on one form. Amending later to include other income will result in penalties and interest that will cost you far more money.

You file ONE tax return with everything included.

You signed on the bottom of the form that you did this.

By not doing this, it created a cluster mess =

you are going to get a refund because of your withholdings but probably have to pay it bad due to not having self employment taxes and taxes on your retirement funds included.

The IRS should penalize you.  But if you fix it before April 15, 2021 they won't. 

Not without paying a lot of money.  You will end up with less money, not more, and they will penalize you.  It is extremely illegal to file any of the three things by itself.  they must all be filed at the same time.  If you file only one of them first, then (1) they can, and should, refuse to send you any refund until you fix what you have done, (2) in theory, although this is unlikely, they can have you arrested for tax fraud, (3) later, you will have to "amend" what you already filed; you can simply file the rest separately, (4) you will have to pay back the difference in between the refund that you got and the smaller refund that you would gotten if you had filed everything at one time, plus interest, plus penalties.

You can only file one tax return, and everything goes on that one return.  Any refund you got form the first filing would be reduced and you would owe back money when you amended your return to include the other stuff.

When you file a tax return, you do so under penalties of perjury.  You KNOW you had self-employment income.  Amending later to declare the income and pay all the taxes you owe gets expensive.  If not paid by 4/15, you will owe penalties and interest.