Minecraft wiki entry for Command_blocks_and_functions, associated text: Using ~ without any number after it in the coordinates counts as zero. Because of the fact that none of those 6 parameters from the last example are used, they will all be defaults.
Note that there are now two types of item slots, Hand and Armor. Hand items are in the order Mainhand, Offhand, while armor items go in the order Boots, Legs, Chest, Helmet. You must even specify empty slots (the { }, parts), unless they're after the last non-empty slot. So, if you want your custom mob to have a helmet, you have to specify all 5 slots, but if it's just boots, you can leave off the other 3. Likewise, if you want them to have leg armor. you have to specify the boot slot, but not chest and helmet slots.
Remember that creatures that burn in sunlight are safe if they have a helmet on, although it damages the helmet instead.
As for the count tag, most codes can get away with leaving it out; however, it is important. An item without a count tag is a stack of zero, better known in the community as a "Ghost Item". A player trying to use a ghost item will have it disappear out of their hands with its first use (which is a failure). While monsters can use ghost items without problem (hence why codes get away with leaving it out sometimes), if they drop the items the player who picks it up won't be able to use it, so it is highly recommended to use the count tag.