What tree is this and how do I care for it? (VIC, Mornington Peninsular)

Hi all,

Just hoping for some guidance on how to help this tree/plant. If you look at the pictures you can see that most of the trees flowers are old/dead and in the whole tree there are only 3 new flowers. I’m not sure whether to cut it back (like cut a few branches off) or if try and manually remove the old flowers..? I think it must be a type of banksia (could absolutely be wrong though).

Thank you for any help!