That is an interesting rifle, and from the photos, it appears to be well made.
@ETipp made some good observations... The single trigger is unusual for a "plains" rifle of this type, but that and the low-profile sights suggest this gun was built for a serious hunter.
There is no way to determine caliber from the photos. As Mr. Tripp said, a caliper type micrometer can give you an approximate bore size, but for a really accurate measurement, it would be worth a trip to a machinist or gunsmith to have the bore checked with plug gauges. I would not remove the breechplug on that rifle, which you would need to do to slug the bore, but slugging it is another good way to determine the size. The little triangular bore gauges that you poke in the muzzle are not reliable. A dial caliper doesn't cost that much in today's dollars and is an essential tool for serious shooters.
Bear in mind, bore size in muzzleloaders means the land-to-land measurement. With American breechloaders, they measure bore size from bottom of groove to bottom of groove.
One of your best resources for getting started may be your NMLRA state Field Representative. This page has them all listed:
NMLRA Field Reps
The Field Rep should be able to get you in touch with a club, gunsmith, or shooter in your area who can examine the rifle, answer your questions, and get you started safely.
That looks to be a nice rifle. Lucky you! Thanks for showing it. Enjoy it safely.
Notchy Bob