Let me get things 100% straight...
Let's assume Larry the Luckless is attacked by a crocodile.
Round 1
Croc bites and hits (doing 1d8+4 bite damage).
Croc immediately gets a free Grapple check to establish a grapple. Success!
Question: Does the Death Roll kick in right now, allowing the croc another immediate Grapple check (for another 1d8+4 damage plus Knockdown)?
Round 2
Croc succeeds its grapple check.
Does it get to do automatic damage (as per the grappling damage rules), plus another check for Death Roll, or must it choose between grappling for damage and Death Rolling?
When grappling a foe of its size or smaller, a crocodile can perform a death roll upon making a successful grapple check. As it clings to its foe, it tucks in its legs and rolls rapidly, twisting and wrenching its victim. The crocodile inflicts its bite damage and knocks the creature prone. If successful, the crocodile maintains its grapple.
I don't think it gets a death roll in the first round. The wording of death roll implies it only kicks in when you make a successful grapple check while grappling. A creature isn't grappling until after it makes its first successful check. The intent of whether or not you get one of grapple's listed options as part of maintaining a grapple in addition to death roll's damage+knockdown isn't clear. I'd probably rule it as giving both, just because crocs deserve to be nasty... it's entirely possible, however, that death roll is only meant to be an additional option you can take while maintaining a grapple (essentially adding a knockdown to the damage option).
How I see it:
Round 1 -
Croc bites and hits, doing 1d8+4 bite damage.
Croc immediately gets a free grapple check from the grab ability and succeeds.
Round 2 -
Croc makes a grapple check as a standard action and succeeds.
It does a death roll for 1d8+4 bite damage and knocks the grappled target prone.
It moves or inflicts an additional 1d8+4 bite damage as part of maintaining the grapple. (Crocs death roll to tear apart prey and to drag them into deeper water where the prey has an even harder time fighting back.)
It happens ins the first round.
Round 1: Bite, grapple check, death roll
Round 2: Grapple check, death roll, bite dmg
Its like constrict
Where does it say Constrict works immediately?
Constrict (Ex) A creature with this special attack can crush an opponent, dealing bludgeoning damage, when it makes a successful grapple check (in addition to any other effects caused by a successful check, including additional damage). The amount of damage is given in the creature's entry and is typically equal to the amount of damage caused by the creature's melee attack.
Format: constrict (1d8+6); Location: Special Attacks.
Constrict says it's an attack which I'd rule has to be the next round since it's already attacked this round. Death Roll would be similar - it says it requires a successful grapple check, it says nothing about that being a free attack like grab does.
Where does it say Constrict works immediately?
It says it right in the constrict description you quoted. Constrict happens on any successful grapple check. The phrase, "special attack," at the beginning is just fluff text and shouldn't be used to arbitrarily modify the ability's mechanics. (Edit) It's also outlined directly in the Bestiary FAQ:
Constrict: When a creature with the constrict universal monster rule (Bestiary, page 298) grapples a foe, when does it deal constrict damage?
A creature with constrict deals this additional damage every time it makes a successful grapple check against a foe. This includes the first check to establish the grapple (such as when using the grab universal monster rule).
—Jason Bulmahn, 11/24/10
Death roll, on the other hand, explicitly limits the grapple checks it modifies by stating, "when grappling a foe of its size or smaller." Grappling is a condition, so you need to have that condition to use death roll.
Constrict and death roll may be similar in that they are both abilities used with grapples, but they are mechanically different and the rules don't support death roll applying to the initial combat maneuver to start a grapple.