It’s not uncommon for the first round loaded out of the mag to be a flyer. As the upper mates, this is less common, but still if the idea is to shoot for groups, put the first round in the dirt, and use the second round that is self loaded threw the rifle cycle as the start of the group.
Now on a new button rifled barrel that has not been hand lapped, the barrel will take a few hundred rounds to start to unify it. This includes knocking down any burs at both the throat and muzzle, unifying the lands and grooves of the rifling, and allowing the barrel to tension unify (stress applied by the button during rifling).
When shooting groups, a 5 to 10 round count is more ideal. Since you are dealing with a auto loader that feeds from two different sides of the mag, and down two different barrel extension feed ramps, the third round flyer may have been caused by a bur in the mag or feed ramp (only caused when the rifle self loaded, and not the initial loading/charging. By shooting a longer string, this gives a better idea on what the rifle/ barrel is doing, and how it deals with fouling (both powder and copper down the bore).
As for the groups starting high, then lowering over time, this could be due to the barrel tension/ barrel installation in the upper settling in threw live fire.
To sum it up, if you were a DCM master shooter, and where having these problems, then we would just blame the rifle. But since it sounds like this is one of your first rodeos with the rifle (type), we are less likely to blame the bad ride on the bull. Looks like its time to cowboy it up, and spend your time putting hundreds of rounds down the bore getting your technique correct before you start riding for points.