Can I use Exarion's priority to drop his attack to 1400? thus bottomless will be activated illegally. And If my opponent activates it before i declare priority, is it still considered to be activated or will it be placed f/d on the field again because it was activated illegally?

No you cannot, Exarion's effect can only be activated during the Battle Step.

Exarion Universe activates in the Battle Step, as wraith said. The timing for that is the same point where you select an attack target (you select what to attack and, before the monster is flipped face-up and damage would be calculated, you decide whether or not to activate its effect)

it can bypass it if you revive it using rope of life and call priority

Let's look at that:

1 - Exarion is destroyed in battle due to it declaring an attack on a monster with greater than or equal attack value.

2- You discard your hand to activate Rope of Life.

3 - Exarion Universe is special summoned to the field with an increase of 800 atk points more (it's now 2600 atk).

4 - You have priority to activate an effect due to a monster being special summoned, however you may not use Exarion's ability because you can not move on to the battle step (where its effect activates) until all chains have been resolved. Exarion is still 2600 and is able to be removed from play with BTH.

Sorry, your strategy doesn't work.

What are you talking about...???

First of all....

Rope of Life
Normal Trap
When 1 of your monsters is sent to the Graveyard as a result of battle, discard your entire hand to activate this card. Special Summon the monster to the field, increasing the ATK of the monster by 800 points.

Second of all...there is no priority in this case...

yeah, exarion isn't your normal priority monster. sure you can use priority with it, but only when you declare an attack (on a defense monster) not when summoned, not even special summoned in the battle phase, since your opponent gets to respond to the summon long before you can declare another attack.

and even if you could do that with rope of life, exarion would still have 2200 ATK and is plenty strong for bottomless to get.

although i beg to question, can you even use bottomless in response to a monster summoned with rope of life? seeing as how rope of life would be activated in the damage step when the monster is sent to the graveyard (same timing as sangan).

No you cannot use Bottomless Trap Hole (or any other "hole" for that matter), in response to the monster summoned with Rope of Life.

Yep...pretty much any effect that requires a monster to be "destroyed and sent to the Graveyard as a result of battle" takes place in the Damage Step.

i didn't think you could, but nobody seemed to notice that the rope of life example was taking place in the damage step.

Yeah...stuff like...

UFO Turtle
Mother Grizzly
Giant Rat
Flying Kamakiri #1
Mystic Tomato
Shining Angel
Rope of Life
Damage Condenser
Option Hunter
etc

...all take place in the Damage Step.