Bf Xt '06 - Brakes Grinding And Other Issues

[NB4C]

I bought my car a month ago from Pickles auctions (ex-fleet / 125000 km / full service history), and recently, I've noticed these issues.

Brakes grinding

> This only happens if I brake gently, I can feel vibrations through the pedal. If I push it hard, it feels firm and doesn't vibrate.

> Usually happens at night or cold day.

> After driving a few k's, the grinding stops and the brake feels normal again.

Diff

> If I reverse and brake hard, I hear a loud thumping noise from the rear of my vehicle, some websites say it's the diff.

Handbrake

> Needs to be pulled quite hard when parking on a slope

It's the first time I've owned a falcon, so are these normal characteristics or should I get my car checked ?