So, there's two seperate questions that could be answered here.
Can you fight unarmed, using primarily punches, and wear boxing gloves? Absolutely. In fact, Unarmed is among the stronger combat specializations in the game, though Boxing Gloves are somewhat weak specifically, because they cause only subdual damage - meaning they will knock your opponent over, but not kill them. Useful sometimes, but rarely.
Can you fight in a 'boxing match'? Well, not per se, however, there are two opportunities for you to engage in a sporting fight for some caps. The Thorn in westside is home to one such opportunity, where you'll have the opportunity to fight off various monsters of the Wasteland such as Radscorpions, Giant Mantises, Deathclaws and Cazadors. Any weapon is fair game in the Thorn, though you're welcome to go in unarmed if you're looking for a challenge.
Male (and only male, the legion are nothing if not chauvinistic) Players aligned with Caesar's Legion meanwhile, have the option to fight in The Arena, located at The Fort. In the Arena, the only weapons permitted are Machete's. All your other weapons are confiscated at the beginning of a match, and you are of course free to use your bare hands instead if you so desire.
Fallout New Vegas doesn't really have a whole lot of weapon crafting, unless you're into Explosives and want to make bombs. In fact, without DLC, there's exactly one craftable weapon that isn't a bomb or mine - the Dog Tag Fist, which you can make with a Repair skill of 30. The schematic can be had from Private Halford at Camp Guardian.
If you have Dead Money, you can do a few upgrades to the Cosmic Knife, turning it into the Cosmic Knife Clean or it's Super Heated variant, or a Knife Spear, which also has a Clean version. You'll need the Repair skill to make these, with 50 being the highest number required, but you don't need any special schematic.
With Old World Blues installed, the only craftable gun in the game becomes available, FIDO is little more than an upgrade to the K-9000 Cyberdog Gun, and is one of the only two weapons for which you'll need a schematic. It's found in the kennel at the X-8 Research center. You'll also need a Guns skill of 75
Finally, Lonesome Road adds the Fist of Rawr. You'll get the schematic automatically when picking up the component parts after killing Rawr, and crafting this powerful fist weapon requires an Unarmed skill of 75.
As for bombs - very few need schematics. Most just need a high Explosives skill, and, in many cases, the Mad Bomber perk and the Gun Runner's Arsenal DLC. You can view the full list of craftable items here. In general, crafting in NV is much more geared towards chems, healing items, food, ammunition, and other consumables than it was in FO3. There are few, if any craftable 'durable goods' of any worth.
Best Answer
I've had this problem on the 360. I'm assuming that it's a bug and not something intentional. I've found that it's usually the weapon. I've "fixed" it by taking the weapon that will not accept the mod and stripping of any mods currently on it. First, I try putting a different mod on, if I can find one. If that doesn't work, I just use the weapon that won't accept the mod to repair another identical weapon. Or, if it's a one of a kind weapon, I would sell it to someone and buy it back. It costs more bottle caps to buy it back than you would get for selling it, which is annoying, but I feel that it's usually worth it. If that doesn't work, and you don't have another mod for that weapon to check, there's a chance that it's the mod, but that's only been the issue once for me. Pretty much every time, the repair or buy back method does the trick for me. Good Luck! (P.S.-I've tried droping the weapon then picking it back up and putting it in a container and then taking it back. Neither of those worked for me but it's probably worth a shot before you go repairing weapons and wasting bottle caps.)