Yes, you can apply for ITINs for your wife and son before you file your tax return. It usually takes about 7 weeks for the ITIN to be issued. You can file for an extension to file your tax return which then you are not required to file until October 15, 2020.
If you have a balance due the amount still needs to be paid by July 15, 2020.
Yes, you are correct that filing as Married Filing Separate does affect the refund or tax due on your return.
How do I apply for an ITIN?