Question about Development of BJJ

As we know BJJ stems from the teaching of Maeda a Kodokan teacher.

So my question is, what about the several Judo kata, did Maeda teach Judo Kata to Carlos Gracie too,

and if yes did Carlos teach these kata (maybe in the beginning of BJJ)?

Ive never seen this. There is a big portion of self defense in Jiu Jitsu which is kind of similar to kata though.

I doubt it. Doesn't seem like something the Gracies would be interested in. Plus, Maeda didn't spend that long with them (2 or 3 years I think) so I'm not sure he would have had the time to teach kata as well.

Maeda was only a 3rd Dan when he left Japan in 1904. Who knows how much traditional Kata he learned.