I mailed in my tax forms and W-2’s to file by mail. How long does it take for them to receive it? Will I be notified once they receive it?

No you don’t get any confirmation for mailed returns unless you got a tracking number from the post office when you mailed it.

4 weeks after you print and mail it, you can start checking IRS Where’s my refund https://www.irs.gov/refunds/