can you claim monthly car repayments as a tax deduction using ABN and log book?

Answer 1

Yes you can, but only if the vehical is primarily for your business, eg if you are plumber or consultant and you have records of the need to use the vehical in everyday business use.

see http://www.ato.gov.au/businesses/default.asp?menu=570

see also
http://www.ato.gov.au/businesses/content.asp?doc=/content/45586.htm&page=8&pc=&mnu=33561&mfp=001/003&st=&cy=

Having an ABN does not always mean you are business though. I believe you need to be over a certain income or turnover amount before you can have a business deduction.