Welcome to Australia in that case, It's my favorite country
1. Doubt many pubs will be showing it mso call around and see but MMA is becoming more popular. You might want to check out CFC and Warriors Realm when they hold events in Sydney.
2. Where abouts are you in Sydney(Send it to me by PM if you if you prefer) but there are some great teams in Sydney like SPMA(Elvis Sinosic, Anthony Perosh), Penrith Elite(Brad Morris, Mark Hunt(Occasionally), Marcelo Rezende), ROOTS BJJ and MMA(Few locations), Gracie Barra Sydney and Maroubra(Bruno Panno), Gracie Barra Manly(Marcelo Rezende). I can give you more if you want.
All have MMA.
SPMA
http://www.sinosicperosh.com.au/
Penrith Elite
http://penrithelite.com.au/
ROOTS
http://www.brazilianjiujitsu.com.au/
Gracie Barra(Bruno Panno) - Sydney CBD and Maroubra
http://www.graciesydney.com/
Gracie Barra(Marcelo Rezende) - Manly
http://graciebarra.simplecohesion.com/