The Detect Magic spell states:
If the aura emanates from a magic item, you can attempt to identify its properties (see Spellcraft).
Identify the properties of a magic item using detect magic: DC 15 + Item's CL
So what, you might ask, is a "property?" Well, they don't define in a legalese way exactly what is included in a magic item's properties, except to note that it definitely gets you command words ("The spells detect magic, identify, and analyze dweomer all reveal command words if the properties of the item are successfully identified..."). One simply has to assume from general English definition and logic that it gives you anything beyond that, including what the item even does.
I think it's best to interpret "properties" as "All of what it does, including charges, command words, and whatnot. Its full rules stat block." (Excepting, of course, other defined exceptions like artifacts and spells on a scroll.) Analyze dweomer specifically says it gets charges, but relying on a 6th level spell to get the charge level of a plain old wand is pretty lame IMO.
In earlier editions of D&D I was fine with not telling people charges and letting them find out when they ran out - it added a nice randomization factor - but in Pathfinder where the Christmas tree syndrome tends to dictate that it's players' God Given Right to liquidate all treasure for a union-decreed cost to buy other gear, not knowing charges and thus value would be an impediment.
No, critical hits must be linked with attack rolls.
I checked with Jeremy Crawford on Twitter and he says that critical hits must come from attack rolls:
@JeremeyECrawford No, since only attack rolls can score critical hits.
In response to @Kevinaskevin Can my Rogue's Assassinate cause my Wand of Magic Missile to crit against surprised creatures?
You should read the full conversation between he and I to get more detail.
Critical hits come up in the PHB on pgs. 194 & 196. As I see it the PHB pg. 194 text doesn't imply that critical hits are exclusive to attack rolls:
If the d20 roll for an attack is a 20, the attack hits regardless of any modifiers or the target’s AC. In addition, the attack is a critical hit, as explained later in this chapter.
PHB 196 describes critical hits but never uses the words "attack roll". Reading the text above someone new to DND could reasonably assume there are other causes of critical hits.
Despite this, Jeremy made it clear that the game designers intended critical hits and attack rolls to be linked.
The wand is more powerful, but only on day one of the adventure, and only with very low level wizards
The Wand of Magic Missiles is more powerful than a low-level wizard, but it's slower to recharge than the wizard's spellcasting, so you can't use it often.
If you cast the level 7 version, or cast seven level 1 versions, your wand is now empty. There's only a one-in-six chance that it will recover all its charges the next day. Most likely, your wand recovers some of its charges, and you now have to wait for it to recharge.
A wizard, on the other hand, can cast magic missile every single day, multiple times per day. When he's higher level, he can still use all his low-level spell slots on magic missile.
The wand can cast magic missile seven times per day - six, if you aren't willing to risk losing this valuable item over 1d4+1 damage - and while that's more than a wizard's 1st level slots, the wizard can also cast magic missile in his higher level slots, so the wand is only really more powerful than a wizard at very low level.
And even then, that's six or seven magic missiles on the first day, then maybe you only recover 3 charges the next day. Now it's got fewer uses than a 2nd level wizard, and on average you'll have to entirely forgo the wand on day 2 of the adventure if you want to to recharge to 7, and even then it's not a sure thing.
The wizard, on the other hand, can keep casting, all day every day, and does not have a 5% chance to burn out when he casts his last magic missile.
It's also unlikely to randomly generate that item when you're level 1. On the magic items chart for level 0-4, the treasure hoard has a 12% chance to give you 1d4 rolls on Table F, which in turn has a 2% chance of giving you that wand. So while any character can be a wizard or sorcerer, acquiring that wand at a level where it's stronger than a wizard is uncommon.