Mundane items can be crafted as per the rules in the PHB, given time and materials, based on the items normal cost. It's up the the DM to decide if any specific tools and/or tool proficiencies are required to do so.
According to the descriptions, all of these focuses are used to channel magic, but are not magical items themselves.
"Downtime Activities," sub-topic "Crafting."(PHB, p. 187)
The general level of effort required is 5 gp per character day spent on item creation.
Yes, you get to reroll a 1 on the attack roll (but must keep the new roll, even if it's another 1)
The gunslinger's Misfire mechanic is described under the Gunsmith feature:
Misfire. Whenever you make an attack roll with a firearm, and the dice roll is equal to or lower than the weapon’s Misfire score, the weapon misfires. The attack misses, and the weapon cannot be used again until you spend an action to try and repair it. To repair your firearm, you must make a successful Tinker’s Tools check (DC equal to 8 + misfire score). If your check fails, the weapon is broken and must be mended out of combat at a quarter of the cost of the firearm. Creatures who use a firearm without being proficient increase the weapon’s misfire score by 1.
The various firearms in the Firearms table for the subclass (which replace the optional ones described in the DMG) have varying misfire scores ranging from 1 to 3. The subclass also grants proficiency with these firearms.
The halfling's Lucky racial trait says:
When you roll a 1 on the d20 for an attack roll, ability check, or saving throw, you can reroll the die and must use the new roll.
As quoted above, the misfire mechanic is tied specifically to attack rolls. Thus, if you roll a 1 on an attack roll with any firearm, you would normally misfire. However, the halfling's Lucky trait means that if you roll a 1 on any attack roll, you can reroll it and take the new roll. This makes it much harder to misfire.
In fact, if you use one of the firearms with a Misfire score of 1 (a palm pistol or a pistol), it's nearly impossible to misfire; as a halfling gunslinger wielding such a weapon, you would only ever misfire if you rolled a nat. 1 on the attack roll, and then got another nat. 1 when you rerolled it (a 1 in 400 chance).
Best Answer
It's up to the DM
The description of the Gunslinger's Gunsmith feature states:
The ability to draft and create firearms using tinker's tools is up to DM discretion, including whether it's even possible and how one would go about doing so. This is true even after the feature gives you the ability to craft ammunition and repair damaged firearms at 3rd level. As such, any such use of tinker's tools before 3rd level would be up to DM discretion, albeit unlikely to work reliably.
Personally, as a DM, I'd probably rule that you don't have a good enough understanding of firearms before you choose the subclass to craft and create weapons using tinker's tools.