I'm reasonably certain that all three are British Army buttons, dating from the late-1700s to early-1800s.
The one with a British royal crown above Old English "manuscript" letters GR encircled by a wreath is definitely a British Army Royal Engineers button.
The same emblem but without the wreath appears to be a "generic" British Army button. Its back indicates it dates from the early-1800s.
Manuscript letters can be very difficult to correctly decipher -- and even tougher when they are on corroded dug buttons. The button you've labeled #6 imight be upside-down in the photo. It appears to have a manuscript letter W or M (depending on the button's orientation) along with another letter. I cannot find a match for it among the hundreds of British Army buttons shown here: Militarynamedregs
I suggest you send the photos of button #6 to the folks at that website, for ID assistance.