For beginners half an hour is usually plenty.  I usually teach on weekdays due to performing commitments at the weekends.  Although I can't guarantee to be available at the same time each week, I try to accomodate my students needs as far as possible.

Some students prefer to learn completely by ear.  Some are happier reading music.  Learning both is best!

Here is a link to a research article which shows that learning by ear benefits every aspect of a student's musical development

"With the “experimental” students surpassing the “control” group in every criterion assessed at the post-test stage, results suggest that playing by ear from a recording may be beneficial for children’s aural development."

Recording machines (like my Zoom H1) are incredibly useful devices for teaching purposes.  It is impossible for a violin student to devote their full attention to the sound they are making - they are far too busy trying to coordinate their muscles.  Being able to play something into a microphone and listen back to it immediately helps students to hear and understand for themselves what they need to work on.  Often students are pleasantly surprised by the sound they make - scratchy sounds under your nose can translate into a healthy projecting tone a few feet away.  Hopefully, this critical listening gives students more musical insight than practising a certain way because the teacher says so. When a piece is ready for performance, we can make a CD quality recording.  These can help students to track their progress over a period of time.  

In repertoire terms, I try to start with my students musical interests.  Alongside plenty of English and Irish folk tunes (from sources such as thesession.org) I also recommend the Suzuki Violin Method books which contain an excellent and varied selection of classical repertoire. Pupils are also learning music ranging from Bach's double violin concerto and intermediate level classical works such as Oskar Rieding's Concerto in D major op.36, some Klezmer fiddle tunes, as well as the odd bit of Jazz and film music such as Pirates of the Carribean with playalong CDs.  As long as a piece is playable on the violin, I am usually happy to teach it.  

For me the internal satisfaction of performing a piece well is usually more important than achieving an exam grade, although I do sometimes coach pupils for grade exams if they wish to take them.   Grade 8 however is a useful mark of achievement, and it also earns valuable UCAS points for University applicants.

I also enjoy helping my students develop their own arrangements of pieces, which can include music they've heard on youtube and spotify. Recent examples include John Williams's haunting theme from Schindler's List, tracks by Greenday, The Levellers and folk tunes by Dave Swarbrick and others.  

For more advanced pupils we can work on transposition and improvisation techniques to build all-round musicianship.

Useful links: