I mailed my tax return back in June and I still haven't gotten my tax return nor both of my stimulus checks. Would these be feasible reasons to call the IRS?

You can get the stimulus money by using the recovery rebate credit on your 2020 tax return so do not call the IRS about the stimulus.

The stimulus check is an advance on a credit you can receive on your 2020 tax return.  If something went wrong or you did not get the stimulus check in 2020, you can get it when you file your 2020 return in early 2021

The Recovery Rebate Credit will be found in the FEDERAL REVIEW section. ( you should see "Let's make sure you got the right stimulus amount”)  If you are eligible it will end up on line 30 of your 2020 Form 1040.

Make sure that you enter ALL of the stimulus money received for the 1st ad 2nd stimulus for yourself, your spouse and your children.

https://www.irs.gov/newsroom/economic-impact-payment-information-center-topic-j-reconciling-on-your-2020-tax-return

https://ttlc.intuit.com/questions/1901539-how-do-i-preview-my-turbotax-online-return-before-filing

Click on Tax Tools on the left side of the screen. Click on Tools. Click on View Tax Summary. Click on Preview my 1040 on the left side of the screen.

As for your mailed tax return:

There have been a LOT of delays with 2019 returns, and it is taking an especially long time for the IRS to process mailed returns.   Did you use a mailing service with tracking--like certified mail-- so that you would know if the IRS received it?   Does the IRS refund site show anything at all for your 2019 return?

 TurboTax does not receive any updates from the IRS. Your ONLY source of information about your refund now is the IRS.

You need your filing status, your Social Security number and the exact amount  (line 20 of your Form 1040) of your federal refund to track your Federal refund:   

https://www.irs.gov/refunds

To call the IRS:IRS:  800-829-1040  hours 7 AM - 7 PM local time Mon-Fri

Listen to each menu before making the selection.

First choose your language. Press 1 for English.

Then do NOT choose the first choice re: "Refund", or it will send you to an automated phone line.

Instead, press 2 for "personal income tax".

Then press 1 for "form, tax history, or payment".  

Then press 3 "for all other questions."

Then press 2 "for all other questions."  It should then transfer you to an agent.