Can you help me with English please?

It means projecting or shining. Often, the path of light can be described as streaming.

The word stream is often used to describe a continuous "flow."

Originally, it meant water, usually fast water. As time went by, the word stream started to mean anything that might come in a continuous fashion such as information or light. Originally, using the word streaming to refer to light was a metaphor. Now light is just one of the things we accept can "stream" because that was how good the metaphor of comparing light to water was. In the same way, most dictionaries have just accepted that "streaming" now means a continuous flow of information, as in "streaming video."

In this manner, they're basically describing that the light almost seems to be forcing its way into the room. That despite the window being small, it illuminates the whole room with light, the way a small hole might let in a lot of water.

As for why "in," well the light came into the room, right? This isn't so much phrasal as descriptive.

Streaming means there is a lot of it. In this context, streaming means the sunlight is bright and that the room is well-lit with sunlight. Another example: If tears are streaming down your cheeks, there are a lot of tears. When using streaming in this context, you're treating the sunlight as a liquid and it is flowing into the room.

The use of in is to indicate the position of the sun. The sunlight is coming from outside the room. Another example: You could say that water was streaming into a tank. If water were flowing in large amount out of a tank, you could say it was streaming out of the tank.

"Streaming in" looks like a phrasal verb, but I am not sure if it is or not. I'm a native English speaker (in my mid-60's) and I've never heard of a phrasal verb until your question.

Hope this helps.

it flow through into them rooms