Targets, and resolving after they change

Two questions sit behind most rulings here. Does this card target, or does it only affect? And if a target changes before the spell resolves, what is left of the spell?

Worked example, targeting. Your opponent controls Baron Nashor, who can't be chosen by enemy spells and abilities. You play Tibbers, "When you play me, deal 3 to all units at battlefields". Tibbers chooses nothing: units are selected programmatically by where they are, not chosen by the controller, so nothing is a target (rule 355.10.d). Baron Nashor takes 3 damage, and a Deflect unit would cost you nothing extra. Compare Falling Comet, "Deal 6 to a unit at a battlefield". You choose a unit, so it is a target, "at a battlefield" is only a restriction (rule 355.10.b), and Baron Nashor is not a valid choice because he can't be chosen (rule 355.9.b).

Worked example, resolving. You play Falling Comet on an enemy unit and, in response, its controller moves the unit to their base. The unit no longer meets "at a battlefield", so it is an illegal target as the spell resolves (rule 359.3.e.2). The spell still resolves, but the illegal target is unaffected and any instruction related to it can't be followed (rule 359.3.e.1 and rule 359.3.e.5). If damage was its only instruction, it has no effect but still counts as played (rule 359.3.e.10).

What targets. A card that chooses specific game objects, players or zones targets them, and one that picks them does not (rule 355.7). To put a spell or ability on the chain, valid choices must be made for all its targets (rule 355.8). A valid target is on the board or the chain, or explicitly in another zone (rule 355.9.a), meets every targeting restriction (rule 355.9.b), and is not the spell itself (rule 355.9.c). Something is not a target when it is in a non-public zone such as your hand (rule 355.10.a), when it is only part of a cost, trigger condition or replacement effect (rule 355.10.c), when it is selected by its characteristics (rule 355.10.d), or when the instruction says a player "must" complete it (rule 355.10.f). A unit that is the only valid choice is still targeted (rule 355.10.d.2). With "any number" or "up to", the player may choose zero and play the spell with no targets (rule 355.13). Damage that is split targets each unit chosen, up to the amount of damage available (rule 355.14.a and rule 355.14.c). A move must choose a destination other than the unit's current location (rule 355.4.a).

Resolving. A target that stops meeting the requirements and then meets them again is legal (rule 359.3.e.3). But an object that changes zones to or from a non-board zone becomes a new object (rule 124), so a target that leaves and returns to its original zone is not legal (rule 359.3.e.4). If only some of an instruction's targets are illegal, it executes on the rest (rule 359.3.e.8).

Ignored and Negated. Instructions that can't be followed because of illegal targets, or because they need unavailable information, are Ignored. Others that can't be followed are Negated (rule 359.3.e.6). A check on an object that is no longer legal returns "null" and the instructions based on it are Ignored (rule 359.3.e.12). A later instruction linked to an earlier one needs it to have executed or been negated (rule 359.3.e.14.a). If the earlier one is Ignored, the later one is Ignored too. If it is only Negated, the later one still executes unless it directly references that action, as "if you do" does (rule 359.3.e.14.b).

Common mistake. "My Deflect and can't-be-chosen units are protected from everything." They protect only against being chosen.