It's not a "C&R" rifle: Collectible and Relic. I believe those are, by definition, over 100 years old (someone correct me if I'm wrong).
No special license: it's a bolt action rifle. I'm pretty sure all states allow it, just have to be over 18, not a convicted felon, and a state resident (and even residency has exceptions). Bayonets, btw, aren't outlawed usually. Yes, semi-auto are available in MOST states. A few very limited areas allow full auto (not sure how, but you can go to 'ranches'). The states that don't allow semi-auto usually allow you to keep what you had before the laws went into effect; however you're not supposed to transport an illegal rifle over state lines.

I've never shot an Enfield. Similar weapons of the time would be the 8mm Mauser (any of the variations of the 3rd Reich), the Mosin-Nagant (1891, M44, or M38 varieties). Perhaps the 1903 Springfield as well. All were bolt-action, large caliber rifles. Comparable "modern" weapons would be similar to a bolt-action hunting rifle firing a 30-06 round or 7mm (though rounds can be argued ad naseum), and I believe those rounds have been around for quite some time too.

Personally, I'm not too worried about a guy with an older rifle. He's accurate, but his rate of fire is such that you'd have a reasonable chance of getting to cover, provided you weren't his first few victims. It's the idiots with the illegal auto's that I worry about!