- Should I send 1040X together with correct 1040NR to IRS immediately? Or should I wait until IRS has processed my wrong return?
There's not really any reason to wait to file an amended return. If you initially had a refund and will owe when you amend, then you might want to wait a bit so you have that refund money in hand before sending it back, but otherwise just get it sorted as soon as you can.
- I am also required to submit Form 8843. Should I attach it to 1040X or send it separately?
Yes, it is meant to be sent with your 1040NR, so when you submit your 1040X and 1040NR include it as well.
- Is it okay to send the amendment after April 15th?
If you will owe additional income tax as a result of the amendment then you should file the amended return and pay ahead of the deadline to avoid late payment penalty. In addition, there can be consequences to not filing Form 8843 on time:
Penalty for Not Filing Form 8843 If you don’t file Form 8843 on time,
you may not exclude the days you were present in the United States as
a professional athlete or because of a medical condition or medical
problem that arose while you were in the United States. Failure to
exclude days of presence in the United States could result in your
being considered a U.S. resident under the substantial presence test.
You won’t be penalized if you can show by clear and convincing
evidence that you took reasonable actions to become aware of the
filing requirements and significant steps to comply with those
requirements.