[RPG] Is a license required for each weapon, or does one cover all

Unfortunately yes; the RAW position is that you need a separate license for each type of Restricted item despite what the other answers suggest. This includes melee weapons (such as the Katana and Shock Gloves).

Core Rulebook, page 419

A restricted item can be purchased, owned, and transported only under special circumstances. You are allowed to purchase and own a gun with the requisite firearms permit, and you can carry it with you with a special concealed carry permit.

Core Rulebook, page 443

Each type of item/activity permission requires a separate license. Things that require licenses include hunting (bow and rifle), possession of a firearm, concealed carry of a firearm (separate license), spellcasting, and any Restricted gear or augmentations, etc.

Note that the second citation clearly indicates that the licenses for Restricted gear are separate from both your Concealed-Carry license AND your Firearm Possession license.

Also, this is a somewhat relevant point regarding jurisdiction. The above ruling, while explicitly spelled out in the book, might only apply to Seattle and/or UCAS:

Core Rulebook, page 419

The legality restrictions in the book use the basic Seattle, UCAS, guideline as their point of reference. Gamemasters should feel free to adjust legality and availability of certain items in other regions of the world as they see fit, and future Shadowrun products may contain alternate availability and legality ratings for different jurisdictions around the Sixth World.

So where do you store all of the things you want to keep? Pictures from your Aunt Edna’s wedding, credit information, your SIN, every book and movie you’ve bought, all the programs you might want to run — all of it fits on your commlink (or cyberdeck if you prefer).

and, more importantly:

A cyberdeck — usually just called a deck — is like a commlink with some extra features. It is a bit bigger than a commlink, about the size of a small tablet or a spiral-bound notebook, or a pair of playing card decks. (...) A deck can perform all of the functions of a commlink, but its primary purpose is hacking in the Matrix.

Are these the robots... err, I mean paragraphs you're looking for? (Emphasis mine.)

Find both quotations on p.223., SR5 core.

I think they pretty clearly indicate that you don't need a commlink if you have a cyberdeck. (Of course, the paranoid decker will probably have a commlink as well. Or two. Just for security's sake. But that's another story.)