Each embassy has its own unique procedures. Some issue the K1 Visa the same day and others process it within a few weeks and have it mailed by courier.
No. Unfortunately, this benefit is only available to U.S. citizens and you must be a U.S. citizens to be eligible to file for a K1 Visa Petition.
The good news is that the USCIS and the U.S. Consulates rarely turn down a fiance visa petition request if the requirements mentioned above are met. The general feeling toward fiance visas inside the USCIS is however, quite negative. Rather than turn down visas, the USCIS ploy is to find some minor error or omission in the completion of the paperwork submitted to them, hold the petition for a month or so, and then return the entire package to you with a cover-sheet telling you what you did wrong. Very often, when you resubmit the petition package with the proper correction, they will again hold it for a month. They then again return it to you with another cover-sheet informing you of a second minor error or omission of which they were obviously aware when they returned your petition the first time! Since we have seen all the errors and omissions, we can avoid this problem for you.
Visa processing can continue in this case if the consular officer obtains a statement indicating awareness of the pregnancy and the desire to proceed with the marriage.
You should make a written request to the embassy asking to withdraw the petition. You may wish to notarize such a statement so we can be assured that you personally are asking the petition to be withdrawn.
After you get married, you have to apply for her Green Card (Permanent Residence, Adjustment of Status). At this time, you must apply for her Advance Parole (USCIS Forms I-131). It takes approx 90 days to receive the Advance Parole Re-Entry Permit after filing. Your fiance must have this before she leaves the U.S. for foreign travel and must present it to re-enter the U.S. If your fiance leaves the U.S. without the Advance Parole Re-Entry Permit, she may be denied entry and the Green Card petition may be cancelled.