You can file a paper return. You still need to fix the problem with the Social Security number in order to file electronically in the future.
No. You can send in the payment at a later date. However, you should be aware of penalties and interest for late payments if you pay past the April 15th deadline.
Yes, your tax return won't be e-filed until you go to the Submit Return for Processing screen at the very end after the Self-Select PIN screen and click the Send Tax Return button. Only the customer can do that. If you want to wait until later in the tax season to file your return and pay your taxes, you can do that. You can also file your tax return now, and wait to pay your tax amount due until April 15th. Just be sure to not forget to pay by the April 15th deadline or you will be subject to penalties and interest from the IRS. After you e-file your tax return, the Check Status/Print Tax Return screen will show all the options to pay your taxes due such as mail in a check with a 1040-V or pay by credit card.
If you owe money to the IRS, you will need to send in your payment by April 15th in order to avoid interest or late payment penalties. However, even if you cannot pay the IRS the amount owed, you should either file your tax return or file an extension by April 15th in order to avoid late filing penalties. Late filing penalties are a lot larger than interest or late payment penalties. A Form 4868 extension, gives you an extra 6 months to file your tax return, but it does not give you an extra 6 months to pay any taxes owed to the IRS.
If you think you might not be able to file your tax return by the April 15th deadline, you should absolutely file an extension. That gives you protection against late filing penalties if you are unable to file by April 15th.
An extension, however, does not protect against interest or late payment penalties. You still need to pay the IRS any taxes owed by the April 15th deadline even if you file your tax return after that date. However, late filing penalties are a lot larger than interest or late payment penalties, so an extension should be filed to protect against those penalties. You can file a free extension on FreeTaxUSA.