You can't use the Hawk Emblem on the gate, but this is useful for carrying BOW gas and Flames.

Not possible on the HD version :(

My bad. Just tested it again and it works. Time to see what I can do with it.

For glitched run you have playing manual, i don't think, that it's useful, maybe you can leave them for final Alexia

After some research, they have no effect on nosferatu and alexia. Which is a shame because this could have been really useful.