Damage on full Life support question

Hello there!

I am kinda new to PoE, and have a question. Didn't find answer on wiki, so. There is support gem "Damage on Full Life Support" (DoFLS) (https://pathofexile.gamepedia.com/Damage_on_Full_Life_Support). Does this gem increase damage dealing on time (DoT)? Wiki page says "It is notably no longer restricted to melee attacks or physical damage specifically."

So, what we have.

1. There are gems skills with "attack" tag, - https://pathofexile.gamepedia.com/Attack. Let's say i use Toxic Rain, which deals damage and then DoT. With DoFLS will Toxic Rain deals more damage during DoT stage? Or it will deal more damage only for arrows fall?

2. Does DoFST increase damage only for gems skills with "attack" tag or also it applies to spells? (Guess only for gems with "attack" tag)

DoFL can only support Attack skills, and gives them More Damage as long you are on full life. If you reserve even 1 life, you will never be full life. If you have CI, you will always have full life (or, well, you are dead).

If you support a Ballista/Ancestral Totem with DoFL, the totem will benefit from the Damage on Full Life as long the totem, not the caster, is Full Life

the Wiki quote you are referring is misleading you. Once, DoFLS was called "Melee Damage on Full Life" and its effect was "+x% More Melee Physical Damage while you are on Full Life". Since that patch, DoFL supports any attack, and will boost any Attack damage.

As for the DoTS, note how the Gem says "More Damage". This is generic, so it will apply to any damage the Attack Skill deals. It's the same as saying "More Damage with Hits and Ailments".
So,

1.
Please note that in order to get the extra damage from the support, you (or your totem) must be full life before the enemy is hit - in other words, if you shoot an arrow, you must be full life when the arrow actually hits the enemy, not when you start your attack. This make Blood Magic tricky but usable even on a Full Life support.

In your case, Toxic rain will deal more damage only if, when each arrow falls, you/the Ballista who shoot it is on full life, not when you/the Ballista shoot it in the sky

2.
No, it clearly applies only to "Attack"-tagged gems.