Does trigger condition don't re-check on resolution but valid target for ability or spells need to re-check on resolution?

Yes, that's correct. The trigger condition itself is only checked once — when the ability would be placed on the chain — and is not re-checked on resolution. Targets, however, are re-checked on resolution.

Once a triggered ability is on the chain, it always resolves even if its trigger condition is no longer true (e.g., the unit that moved is now dead or back at base). The ability doesn't "fizzle" just because the event or state that caused it to trigger has passed (FAQ #6035, #6550).

Targets work differently. Rule 359.3.e.2 says a target is illegal on resolution if it no longer meets the spell or ability's targeting requirements, or if it changed zones to/from a non-board zone. If a target becomes illegal, the instruction that targets it simply does nothing — though the rest of the spell/ability still resolves as much as possible (Rule 359.3.e.5–8).

There's a third layer too: referents like "here" or "my Might" are checked on execution (Rule 359.3.f.2). So even though the trigger resolves, if it says "deal damage equal to my Might" and the unit is dead, "my Might" returns null and that part does nothing. The ability still resolves — it just has no effect on that portion.