I will be moving to a temporary residence shortly after tax deadline for several months, but then out of country for another couple of months before moving to another state. I don't want to miss any mail during the next half year so can I have them send any correspondence to my family's home (abroad) instead?
The link below gives you some information about using a foreign address in TurboTax:
https://ttlc.intuit.com/questions/1900705-can-i-e-file-with-a-foreign-address
I worked in one state all of 2018 so will using a foreign mailing address affect the filing?
No, it will not affect your return, however there are some restrictions regarding foreign-address returns:
IRS regulations require a U.S. bank account to receive your tax refund, and you'll need a U.S. bank account (or credit/debit card with a U.S. billing address) if paying additional federal taxes owed.
Like many stateside merchants, we require a U.S. billing address to pay for TurboTax if using a credit or debit card.
If you're deducting fees from your refund with the optional Pay With My Refund service, you'll need a U.S. address.
Some states also let you e-file with non-U.S. addresses. We'll let you know if your state supports this.