Yes, you may grapple as part of a charge
This can be seen on the combat chapter (SRD reference, Table: Miscellaneous Actions):
2: These attack forms substitute for a melee attack, not an action. As melee attacks, they can be used once in an attack or charge action, one or more times in a full attack action, or even as an attack of opportunity
Yes you can charge and then grapple instead of attacking
The use of charge allows you to make a single melee attack (which can be replaced by your grapple) after your moving with a +2 bonus to attack, which also applies to your grapple check.
Attacking on a Charge
After moving, you may make a single melee attack. You get a +2 bonus on the attack roll and take a –2 penalty to your AC until the start of your next turn.
The grappling description you have linked goes as follows:
Starting a Grapple
To start a grapple, you need to grab and hold your target. Starting a grapple requires a successful melee attack roll. If you get multiple attacks , you can attempt to start a grapple multiple times (at successively lower base attack bonuses).
The condition of requiring a melee attack is met for the grapple through the charge as well.
However be careful, as you are provoking an attack of opportunity on the target you are attempting to grapple and have -2 penalty to AC until the start of your next turn through the charge.
Attack of Opportunity.
You provoke an attack of opportunity from the target you are trying to grapple. If the attack of opportunity deals damage, the grapple attempt fails. (Certain monsters do not provoke attacks of opportunity when they attempt to grapple, nor do characters with the Improved Grapple feat.) If the attack of opportunity misses or fails to deal damage, proceed to Step 2.
Following the grapple rules, you are compelled to do repeated opposed grapple checks during the grapple, depending on the action.
Grapple check is like a melee attack roll. The check is: Base attack bonus + Strength modifier + special size modifier. (note: after the charge turn, the +2 bonus to attack rolls will no longer apply to the checks as your charge is over and you are in grapple status)
Special size modifier is as follows: Colossal +16, Gargantuan +12, Huge +8, Large +4, Medium +0, Small -4, Tiny -8, Diminutive -12.
Yes, you can. A grapple can be used instead of any melee attack:
Starting a grapple requires a successful melee attack roll. If you get multiple attacks, you can attempt to start a grapple multiple times (at successively lower base attack bonuses).
Since the attack at the end of a charge is one of those, you can grapple instead of the usual effects of attacking. The +2 bonus to attacks you get for charging also applies.
I’m not aware of anything that says this explicitly, however. The only thing I can point to is the grapple rules saying they replace an attack, that grapple checks are “like” attacks (and carry on any iterative penalties, anyway), and nothing about charging says you can’t grapple. It certainly also seems to make narrative sense, to me anyway, so I don’t see why they would restrict it, which encourages me in believing that they didn’t intentionally.