If I apply in Australia will I be able to work?

To apply on shore for P.R. you must have a substantive visa. That is a visa which is NOT a bridging visa. The conditions set in your substantive visa for work and study will apply to the bridging visa which is given to you until your EEV is granted. Once the EEV is granted you will be able to work and claim Medicare benefits.

If you need to work whilst you are on a Bridging visa you can apply on form 1005 for "Change of Conditions" and if the work restriction is lifted you can get a Tax File number and a Medicare card.