No bow hunting? That seems odd, I would expect in Europe (not the friendliest place for gun ownership) that hunting with firearms would be what is vorboten. Have the powers that be in your country explained why?
By the way, if you make it over here and find yourself in Albany, Ga in the next year and a half, I'll take you out hunting! There's even a group around here that takes people on pig hunts at night with night vision optics on the guns. Pigs are a nuisance animal (they eat crops) so there are no limits, no restrictions as to what you hunt them with, and no restrictions as to when you hunt! The name of the group is Hog SWAT (SWAT being the abbreviation for Special Weapons and Tactics - normally your special group of police officers with that sort of training.) They contact farmers who allow them on their land. This reduces damage to their crops. I haven't done it myself but it sounds like a blast.
Hunting with firearms is not "verboten", laws about hunting are different from country to country, here in Luxembourg it'll you take around a year to get your shooting license because you have to go to courses to learn everything about the fauna, then they test your knowledge and make a shooting test & when you pass you get your license to hunt.
With this license you're allowed to buy rifle, to get a rifle you go to an arms dealer there if you found a rifle you fill out governemental form,
pay a stamp who cost 17€uros (around 20 $), the dealer will send your inquiry form to the Ministry of Justice.
Then you will be checked by the governement and if your criminal record is blank you will get your firearm license wich allows you to carry that rifle from home to the hunting place.
Night hunting is verboten, handgun hunting is verboten too
I own a license for sports shooting (the procedure to get it is the same) wich allows me to carry my long or short gun's unloaded to the shooting range, and every time you want buy a new gun it's the same procedure you send in your old license pay a stamp(17€) and if you're lucky you'll have your new license after 2 weeks.
Here in Europe we have strict gun laws but here in Luxembourg we're still lucky I can buy as much guns I want even fullauto guns, in france for exemple you can't buy a military rifle in the original caliber, for exemple an AR 15 in france you'll get it in 222 not 223.
The germans have the strictest gunlaws for exemple as an german you already own a 357 mag revolver and you want another one then you've to explicate them why you are in need of a second 357 mag, the same for another rifle in the same caliber.
Like I wrote in my previous post be happy to be an American 
Thanks for the invitation that would be great, I plan to visit my friend Tom next year he lives in new hampshire, I might make it over to albany, we'll see.