You would definitely get to be there for all of M3, then I'm not 100% sure how the site handles fourth year but I believe you would be able to stay for electives and stuff that year too!
Rank lists are not due until February. A very general timeline is that ERAS opens up around June or July when you're starting your M4 year. You will likely take Step 2/Level 2 around then as well as you are given a month off to study in June between your last rotation of M3 and the start of M4. ERAS submission date is typically end of September, so you'll have time to fill out the application and gather things like your board scores, transcripts, letters of rec to submit. Most people will do auditions from the beginning of M4 (so typically July) throughout December, with the target being July-October so you can rotate there before apps go out. Then from October-January you'll get invitations to interview at programs. Come February, you'll submit your rank list of all the programs you interviewed at, and each program will submit their rank list of applicants they interviewed. Then March is match day! So basically since rank lists aren't due until February, you can do an audition up until that point if you want to get one-on-one exposure to a program, but ideal time is July-October so that you can convince them to give you an interview if you perform well!
*caveat here being that advice on auditions etc. is dependent on what specialty you're applying to/your competitiveness as an applicant, but that is getting more into the weeds and isn't really relevant at this stage in the process