If it gives you a box under your health bar, it's a status. If not, it's not a status. Weak, curse, blind and the like are gonna be status effects and can be removed. I believe that burn and bleed can also be removed. But it isn't a potion of purity. If you are standing in a fire, you will still burn, and you still take damage from normal sources like poison clouds.
Beating Tengu consistently on 0 chal more comes down to resource management and preparation. Phase 1 basically measures 2 things, your survivability and memory. (If you are hitting the traps then that's not a cleric issue). Good gameplay up to this point should have rewarded you with at least 1 health pot, unless you are rocking cloth armor phase 1 will only be an issue for you if you were making poor decisions up to this point.
Phase 2 is understanding how the attack patterns work. Getting mobility in the form of chains, blink stones, or even swiftthistle will help you avoid traps and close in on Tengu. Just time these utilities so you aren't instantly forced away from Tengu when you get close. In the very unlikely event you have found no mobility of any kind up to this point, use your ranged spells to chip away while you shuffle your way on up to smacking Tengu in the face.
Early floor bosses are less about the character you are playing and more about understanding the mechanics of the game. I would argue that the cleric has a higher skill floor than other adventurers, but he certainly isn't weaker.
This is in the beta. I can't tell if this floor generation is intended game design or not. Yes I already searched for any hidden doors and there are none.
Personally, I utilize a flamethrower, but to each their own.