You can still keep track of it even if the card does not explicitly say so; the marker you use to keep track of it is not itself a part of the game, though.

Permanently? That kind of thing is very annoying to track without a token or aura

­Rod of Ruin was to cast and to activate, but then again it was never really that great.

It should be noted though that not having a mana cost at all associated with the activation is a meaningful boost to the strength of this kind of effect.

NR: I think this could still do with some more juice. Options a. +2/+2 for each creature that shares a type b. Also give an ability (ideally some form of evasion)

Probably not mythic

Is a 4 mana uncommon a bit less overpowered?

2 mana noncreature source which can ping each turn is deceptively strong and oppressive to the point of format warping (ala how for example bowmasters has been pushing out classics such as bob from legacy top tier status).

NR: Love the flavour! I think a catapult ought to kill the creatures it gives flying at the end of the turn (or at least, do some damage to them. Lean into the flavour!)

NR: Healing is normally white rather than green. X comes first in mana costs (it's a bit weird, but we say mana costs in the opposite order to how they're written). Powerwise it's fine to have just a flat payment instead of an X, and it would give you space to say what happens instead of the dying (thought the modern way would be: R/W, sacrifice Emma: target creature gains indestructable and hexproof until end of turn.

NR: Are rabbits going to block a flying thing very often?