Mammoth flea entry errors?

So I was looking at the mammoth flea.

Its offense looks lite this:

Speed 30 ft.
Melee bite +4 (1d8+3 plus blood drain and disease)
Space 10 ft.; Reach 10 ft.
Special Attacks blood drain (1d2 Con), disease

First, I'm confused by blood drain. The universal monster rules on Blood drain states the following:

Blood Drain (Ex) The creature drains blood at the end of its turn if it grapples a foe, inflicting Constitution damage.

Format: blood drain (1d2 Constitution); Location: Special Attacks.

I'm inclined to believe Paizo has taken a very roundabout way of saying that the flea deals 1d2 Con damage with its bite, but I'm not sure. Does the feal have to grapple its opponent in order to drain blood?

Secondly, where's that damage and attack bonus coming from? Take a look at its statistics:

Str 13, Dex 17, Con 13, Int —, Wis 11, Cha 6
Base Atk +3; CMB +6; CMD 19

With Str +1, BAB +3 and a size modifier of -1 its bite should be +3 (1d8+1), right? Or am I missing something?

The same goes CMD and CMD. Those doesn’t look right.

For the bite attack, I believe you are correct. It should be +3. I get +3 BAB, +1 Str, and -1 for size. I see no Weapon Focus feat or other such modifier. So I would say that is an error. Be thankful they didn't give it Weapon Finesse as a bonus feat instead of Dodge, I suppose.

For the damage, I also only see a +1. Even with Strength and a half for being the only attack it would still be +1. Unless this is just bonus damage being added ad-hoc because the creature description says their bites are 'excrutiatingly painful' then that would be another error.

For the Blood Drain, typically you use the Universal rules unless the creature entry indicates otherwise. A tick swarm, a nosferatu, a giant leech, and a mammoth flea likely have different ways to drain blood. In this case, it appears to happen on a successful bite. I don't see any a specific Blood Drain entry for the mammoth flea (going from the link you posted) and since I no particular mention of it grappling, grabbing, or attaching, I will assume the indication of Blood drain in connection to the bite attack is sufficient.

This is similar to how creatures with Improved Grab might be able to grab larger or smaller creatures than would otherwise be indicated by the Universal ability description. Some can do it up to one size smaller or to creatures of equal size or occasionally even to targets of up to one size larger or regardless of size difference. To me, it looks like the drain is in addition to the bite.