Is interleaving used in MIMO?
The colouring of those data bits is figurative. It's far, far more complicated than that. That diagram is what's known known as a Lie to Children. It's the sort of diagram that would be shown in a presentation to politicians when trying to get them to license spectrum to your organisation.

Does each parallel data stream carry some of the data?

Yes

Is the data stream taken apart in some way before sending out on the MIMO streams and then reassembled afterwards?

Yes

Is the mean data rate on each parallel stream lower than the mean data rate on the original and recovered streams?

Yes

Does MIMO take 1 bit at a time and multiplex them strictly between the four streams?

Absolutely not.
I fell foul of a lie to children when I was a child. My shape-sorter I used when I was pre-school had nice regular polygonal prisms to bash through holes, a square, a circle and a regular triangle. Later on in my maths lessons, I insisted that a triangle had three angles of 60°. I was convinced I was right, I'd seen it in my shape sorter. I would not believe the teachers who told me that a triangle could have different angles. I even had stand up arguments with them in class, at the age of perhaps 8. It inhibited my learning geometry.
Those one bit per channel pictures are the nice easy 60° angles of a kid's shape-sorter. But we have isosceles triangles, right triangles and scalene triangles, which correspond to the several layers of message encoding, packing, forward error correction, HARQ processing, matrixing that is not shown on this diagram, and which certainly does not work one bit at a time, which the word 'interleaving' seems to imply. These work in blocks or chunks of data. That is needed to ensure correct message transmission over a medium that isn't 4 channels for 4 antenna at the best of times, varies, and is unreliable. With 4 antennae you might get approaching 4 streams in a lab environment, 3 is good for out in the field, and you can generally expect more than 1.
Looking at your diagram, one of the lies is that the red antenna sends a signal to the red receiver and so on. That's the same sort of level of incorrect as the input stream being taken a bit at a time to each channel. Each TX antenna sends signals to all the RX antennae. The data is matrixed onto all the transmit streams, and is deconvolved at the receive end. The logically distinct channels are created mathematically from the different views of the single channel that each antenna has. See this Q&amp;A for a bit more detail on how the RF channel is handled to create multiple logical channels.