The product you are describing is the 4th Edition Dungeon Master's Kit

This was released midway through 4th edition's release and included a book as well as some maps and tokens. Unfortunately it is out of physical print. You can buy the book only as a digital PDF here.

There is no "Dungeon Master's Kit" for 5e that has been released or is scheduled to be released before Christmas 2014.

Keyword is "kit" which generally means a book, some dice, and some tokens/figures to aid in the visual representation of play.

The 5th Edition Dungeon Master's Guide will release shortly

The DMG will be out December 9th. It is simply a book, a big one, covering lots of rules and providing a ton of setting and optional rules for 5th edition.

4th edition and 5th edition are similar but different

Both tell stories about heroic adventurers but the framework they use to tell these stories and engage the players is different. There is a tonal shift in focus for the rules between editions. The 5e DMG is not compatible with the 4e books.

Buying all 3 books will ensure your son and his friends will be able to play the new edition.

If you do pick up the 5e Player's Handbook, Monster Manual, and Dungeon Master's Guide they will have everything they need to play 5th edition.

There are a few official miniatures out for 5th edition currently but they are not available online.

Wizkids partnered with WOTC to make plastic miniatures for 5e, but they seem to be only available in game shops. You may want to check out a local game/hobby shop as they have these or other fantasy miniatures that he could use.

However any miniatures your son already has are perfectly usable with 5th edition.

It's up to you

There are two play styles (with regard to this question at least), with their own drawbacks and advantages.

The first is to keep the realms of the world (DM) and the player characters strictly separate. I use the term "Golden Box" to describe this. In Golden Box gameplay, the players cannot define anything about the world, including who an NPC does or does not know - that is in the purview of the DM. Similarly, the DM cannot define background for the player character.

The advantages to this method include not having to deal with this sort of question. The player only knows the NPC if you, the DM, say they do. The player can argue for it, usually backed up with a background, but in the end it's up to you.

The disadvantage to this is that there is very little flexibility, and the players can feel like they have very little agency over the game.

The second playstyle, which I will not name since the only name I know it by lacks general context, allows anyone to define anything, and it is only addressed if there is an issue or will be an issue if left unchecked.

The advantage to this kind of play is that the players usually have a lot more buy-in - they have created parts of the world. In situations where this is taken to its logical end, the players define the world, the npcs, and to an extent the antagonists. This can be a very satisfying way to play.

The disadvantage of this is primarily it gives 'that guy' a free pass for a long time (to wreck your plot), and it can make a game feel directionless.

These are extremes. You usually mix them when playing a game.

I would recommend, in your situation, that you tend towards the first. When the player declares something about the setting that gives them an advantage, have them justify it, or if the situation allows, to roll for it. Don't be afraid to say No, especially if the declaration the player makes is problematic.