Can you especially keep a fast to pray for Palestine or would that be an innovation?

So it's very important that the primary intention is doing it for Allah subhanahu wa ta'ala. Now you could have a secondary intention that we know the dua of the fasting person is accepted, the hadith collected by Tirmidhi, so you're going to fast and whilst you're fasting you will make dua for the Palestinians, there's no issue with that. And you could also have a secondary intention that it's also going to raise awareness of their current situation. So as long as you have those secondary intentions, but the primary one, remember, is you're doing it, seeking the reward from Allah Subh'anaHu Wa Ta-A'la, then that's fine.