I'm 5'1" and I was just cast as Tzeitel.
Of the other four girls, Shprintze is closest to my height... and she's Asian. Hodel and Bielke both have a good seven inches on me, haha. So it all depends on your director, really!
As for audition songs, I was kind of stumped too because Fiddler has such a unique style. I ended up using Meadowlark from The Baker's Wife and got called back for pretty much every role but Fruma-Sarah. If you're going for one of the daughters, anything that's melodic and shows off your acting should work, as long as it's not too contemporary-sounding.
Other songs that other people who got cast used were:
Will He Like Me? or Vanilla Ice Cream (She Loves Me)
Once Upon a Dream (Jekyll & Hyde)
If I Loved You (Carousel)
Falling In Love With Love (Boys From Syracuse)
Yes, My Heart (Carnival)
Break a leg!