Yes they COULD be modern. And yes the one is for sure a 45 cal. Colt developed the Army 45 in 1911. HOWEVER, the 45 cal bullet was developed by Browning in 1904.
The smaller one is a pistol round. Could be .38 cal or 357 magnum or a 9mm. Without knowing the diameter it is hard to say.
It sure might have been illegal to discharge a firearm in the city, However, my father used to shoot his shotgun off the porch for New Years and some people love shooting signs even though illegal.