Re: master's program or master program
The 'master's program' is correct, in my view. The 'master program' makes it sound like there are a number of different ecology programs and the one you are applying for is the top/main/best one. You will also hear 'I'm doing a Master's in ....', again with the 's.
'Master', without the 's is often heard in phrases like 'the master bedroom' (the main one of several), or 'the master key' (the one that opens all the rooms), for example.
I hope this helps.