Should i protect a birds nest outside our bedroom window from the rain and how?

No, you should leave the nest alone. Wild birds are very skittish around humans, treating humans as predators, and may abandon the nest if the scent of a human becomes too close. This would result in any eggs already laid in the nest also being abandoned and dying. The birds that built the nest either expect the nest to be protected from the rain or are adapted to sitting out the rain on the nest.