Am I supposed to show up to new unit with unit patch?

I would just verify the unit patch and have it ready. Or pop into supply and they’ll issue you a few. Not a huge deal if you’re new

you wait till they give it to you

Put it on! You’re in the big army now

It depends on your unit honestly, my first unit reamed me for it but my last unit couldn’t of cared less. Given I was the first soldier for my last unit so my CW3 (acting CO) wasn’t really paying attention to anything like that.