Yes, you can still apply to the program. The basic requirement is that you are a student at a US degree granting institution. However, you should know that if you are not a permanent resident at the time of appointment, the NIH will only support J1 visas.
You get the opportunity to meet the PI and members of the laboratory PRIOR to the official interview. This provides valuable information about the lab, allowing you to determine it the lab is a good fit before accepting an offer. In addition, investigators hold the accepted applicants in high esteem, as they are competitively selected for the program
No, acceptance does not guarantee a position. However, the chances of receiving a position are higher than if you were to email investigators yourself to inquire about open positions.
Perhaps, the structure of your interview is dependent on you and the PI at the time of scheduling. Most applicants set up 30-60min meetings, where they learn about the PI, lab, and possibly meet lab members. An official interview is typically a half day, where in addition to speaking with the PI and lab members, you also present a job talk. Roughly 50-70% of the GSRP applicants go on to have official interviews after the program. Whereas 10-20% receive job offers immediately following or during the program.
Roughly 40-50% of applicants accept postdoc positions.