Yes you don't have to file but you can go get back any withholding taken out in boxes 2 or 17.  But you don't get boxes 4 or 6 back.

To file a separate return as a dependent you need to set up a new account.  Online is only good for one return per account.  You can use the same email address for 5 accounts.  You can probably use the Free Edition or the Free File website

Https://ttlc.intuit.com/questions/1894512-how-do-i-start-another-return-in-turbotax-online 

Be sure on your return they check the box that says they can be claimed on someone else’s return.  If their only income is W2 and under 12,200 they do not have to file a return except to get back any withholding taken out.

Filing requirements for a dependent

https://ttlc.intuit.com/community/children-dependents/help/do-i-need-to-file-my-own-taxes-if-i-m-a-d...

But if I didn’t have my taxes withdrawn automatically from the beginning, I could’ve essentially kept the money taken form things like social security tax?

You cannot avoid SS & medicare taxes from being withheld ... however you can stop the fed & state withholding so you don't need to file a return to get it refunded.  

No.  It's mandatory that they take out SS (6.2%) and Medicare (1.45%).  If you think you will make less than 12,200 total for the year you can stop the federal and state income tax withholding.

How would I be able to get my state tax back? I tried filing but was only able to get my federal tax back.

You are able to prepare a state return when you prepare your federal return. If you did not prepare a state return yet, log back into your return and click to add the state you need to file to the return. Prepare the return, and then you can file it.

If you have prepared your state return and you are not able to file it yet, it is because your state has not opened up the e-filing option yet. Even though the IRS has started to accept e-filed starting 1/27/2020 there are some states who have not finalized their tax forms yet, thus not opening the e-file option.

Click here to look up your state and see when all forms will be ready: https://ttlc.intuit.com/community/forms/help/state-forms-availability-table-for-turbotax-individual-...

Once the forms are ready you will be able to e-file your return and check the status here: https://ttlc.intuit.com/community/return-status/help/how-do-i-check-my-e-file-status/00/25538

If you prepared your return and you are not due a refund, but owe the state more taxes, you may not be required to file a return if you made under your states threshold. You can see what the requirements are for your state by visiting your states department of revenue website.