Is it valid not to specify the type of intention before an act, such as giving a gift or donating money with the intention of earning reward from Allah without pinpointing the type of intention, and would there be a reward for that?

In absolute voluntary acts, the intention of volunteering suffices. The more good intentions there are in a single act, the greater the reward. Al-Bahuti stated that intention is the heart's resolve to perform an act of worship seeking closeness to Allah Almighty. Abu Talib al-Makki held that good intention is the basis of reward, and that the recompense for deeds multiplies with the multiplicity of good intentions. Al-Ghazali affirmed that acts of obedience are linked to intentions in their validity and the doubling of their merit, and that a single act of obedience can carry multiple intentions, with each intention yielding a reward that is multiplied tenfold.