"Sometimes there is the rainbow after rain." - Why should it be "the" rainbow? Is ther one particular rainbow that comes after rain, while all other sorts don't? Sounds weird.

sometimes after the rain is a rainbow?

Sorry, the Polish sentence is factually incorrect.

I'd accept "Sometimes with the rain there is a rainbow" - but that doesn't translate po. A rainbow needs Sun and rain (or other water droplets, e.g. a waterfall) at the same time: it's simple school physics.

Of course, it might have stopped raining where I am: if it's still raining somewhere between me and the Sun, I'll still see the rainbow.