What time of horse is he? My haflinger would rather do a spanking trot than gallop, but she is gradually learning that she can go faster and I find riding in company helps. A gallop is a 4 beat pace and much faster than a canter, they really open up and flatten usually, or at least my TB does and we have hit 40mph
Yes, take weight out of saddle and lean forwards slightly
(english riding - can't comment on anything else).