Despite what people might think, it is not legal to shoot trespassers in America either. You can only use deadly force in self defense. A guy walking across your lawn is not a deadly threat, even in America.
Before telephones and automobiles, rural landowners were on their own to defend themselves and their property, the county sheriff possibly being hours away; at a minimum it was prudent to be armed when confronting a trespassing stranger. It might be reasonable for the landowner not to risk engaging in an attempt to bodily subdue and evict someone, especially when there was no practical way of keeping them from returning. Often the firearm in question was a shotgun which could have a “less lethal” load- birdshot or rock salt. And if it was a case of theft, then the landowner had the right to attempt to prevent the commission of a felony on his property. That said, the stereotype of the paranoidly reclusive farmer who shoots on sight is an exaggeration: someone who did that would at a minimum get a visit from the sheriff and possibly be jailed on charges.
Note that breaking and entering is a felony completely aside from mere trespass, which is almost always a misdemeanor.
You might find this earlier thread of interest: Why didn’t Torrens title catch on in the US?
Right. An adverse possessor will never be the recorded title holder until an action for quiet title or ejectment (or probably some other weird common law action I’ve already forgotten) is filed and adjudicated. That doesn’t mean they don’t have actual title to the land, though. The deed is a formality, which in and of itself is not dispositive.