What happens if a caster casts Feign Death on himself and another caster (that believes that the first caster is really dead) try to cast a resurrection spell? Does the second caster understand that the first one is not really dead?
Nothing happens, the spell slot is expended, and the caster perceives that nothing was done to the target.
The second caster would see that the target was unaffected, but would not immediately know why.
Xanathar's Guide to Everything Offers Guidance on Invalid Spell Targets
XGtE p.86 :
If you cast a spell on someone or something that can't be affected by the spell, nothing happens to that target, but if you used a spell s lot to cast the spell, the s lot is still expended
Since resurrection does not require a saving throw, the caster just knows the spell did nothing:
Otherwise, you perceive that the spell did nothing to the target.
The guidance on spells requires saving throws is informative about not giving away the invalid nature of the target.
... the invalid target appears to have succeeded on its saving throw, even though it did not attempt one (giving no hint that the creature is in fact an invalid target).