Hello there. In the last adventure in whaterdeep I've lost an arm insed of a mimic while I was trying to save a friend putting a molotov granade inside of the monster. I really would like my arm back.

The fun thing is that my character is a gunner gnome who owns a shop we're I sell weapons and mechanical things. So my idea was to install my self an artificial arm.

Can anybody tell me what I need to craft one?

In that mimic I've also found a blue print of a tesla gun. Can I insert that in my arm? 

These are questions you need to ask the DM. There are no rules that cover this so this will be entirely a DM thing and no advice we can give you is going to be helpful in that regard since it depends completely on what your DM thinks. We can offer suggestions, of course, but it's your DM who would need to come on here and read them and make their own decision.

As my suggestion I would follow the rules on crafting a magic item, and consider an ordinary arm to be equivalent to uncommon with anything extra bumping up the rarity (and therefore the cost and time).

There's also the Regenerate spell if you just want your arm back and even if none of your party can cast it, a simple adventure to find somebody who can will provide the easiest and fun way to regain your arm.

I'd say you should first talk to your DM, I don't think there are firm rules on that.

I would compare the effects of existing material and equate accordingly.

Regenerate would restore your arm. A spell scroll with that spell is 25000 gp in materials and 16 workweeks of effort.

I would let you design your own arm and build it in the same time and for the same cost.

For the tesla gun it would be similar. What does it do, can it be compared to an existing effect?

But really, that should be a chat with your DM.