First, it will be better to file jointly, since you will get a larger standard deduction (as you've already noticed, it does make a difference in the amount you owe, or are getting back).
Yes, you can apply for an ITIN for your wife when you send in your return. You cannot e-file when you do this, because the ITIN application must be accompanied by documents proving her identity. The easiest thing to do is to use her passport, assuming she has one. However - you would need to include either her original passport (which I would not recommend sending through the mail), or a certified copy (which you can get through an embassy or consulate). Alternately, you can apply for the ITIN in person using an IRS-authorized CAA (Certifying Acceptance Agent). The IRS website has a list of CAAs by state.
Yes, you still need to file form 8843 for your wife.
