[RPG] Does the Gunsmithing feat let you make a gun without Crafting it

Yes

The feat removes the need of using the Craft skill to make guns or ammunition.

The availability of the feat (and firearms in general) is entirely up to the GM. In a setting where firearms exist but are rare, the feat might not be available. As such, anyone interested on making guns or ammo must use the old fashioned way, the Craft skill.

In another setting firearms are common, people who are gunslingers have enough knowledge (and technology) to be able to make their own guns and gunpowder much easier and just spend enough money and time, no special skill required.

For alchemical ammunition, you require at least 1 rank in Craft (alchemy), as explained on the feat:

Crafting Ammunition: You can craft bullets, pellets, and black powder for a cost in raw materials equal to 10% of the price. If you have at least 1 rank in Craft (alchemy), you can craft alchemical cartridges for a cost in raw materials equal to half the price of the cartridge.

Anyway, the point is that the availability of each of the firearms mechanics depends on how rare the GM wants firearms to be. This is explained in the Ultimate Combat under the firearms rules:

No Guns: If you do not want guns in your campaign, simply don’t allow the rules that follow. The Pathfinder Roleplaying Game plays perfectly well without them.

Very Rare Guns: Early firearms are rare; advanced firearms, the Gunslinger class, the Amateur Gunslinger feat, and archetypes that use the firearm rules do not exist in this type of campaign. Firearms are treated more like magic items—things of wonder and mystery—rather than like things that are mass-produced. Few know the strange secrets of firearm creation. Only NPCs can take the Gunsmithing feat.

Emerging Guns: Firearms become more common. They are mass-produced by small guilds, lone gunsmiths, dwarven clans, or maybe even a nation or two—the secret is slipping out, and the occasional rare adventurer uses guns. The baseline gunslinger rules and the prices for ammunition given in this chapter are for this type of campaign. Early firearms are available, but are relatively rare. Adventurers who want to use guns must take the Gunsmithing feat just to make them feasible weapons. Advanced firearms may exist, but only as rare and wondrous items—the stuff of high-level treasure troves.

Commonplace Guns: While still expensive and tricky to wield, early firearms are readily available. Instead of requiring the Exotic Weapon Proficiency feat, all firearms are martial weapons. Early firearms and their ammunition cost 25% of the amounts listed in this book, but advanced firearms and their ammunition are still rare and cost the full price to purchase or craft.

Guns Everywhere: Guns are commonplace. Early firearms are seen as antiques, and advanced firearms are widespread. Firearms are simple weapons, and early firearms, advanced guns, and their ammunition are bought or crafted for 10% of the cost listed in this chapter. The Gunslinger loses the gunsmith class feature and instead gains the gun training class feature at 1st level.

Keep in mind that a gunsmithing kit provides all tools necessary for the job, and is required regardless of the rarity level.

This small kit has all the tools a person needs to create, repair, and restore firearms, except for the necessary raw materials. Without such a kit, you cannot properly construct or provide upkeep for firearms.