Not at all, I hadn't even heard of it before. I can, however, give you some synonyms to "consider." "I'll consider it." "I'll think about it." "I'll think it over." "I'll weigh my options." "I'll brain storm." "I'll contemplate it."

No - I've never heard of it before. The Collins dictionary says it is normally used facetiously.

For a moment, I actually thought "cerebrate" was a typo for celebrate. :) No, it's very uncommon. We would understand it as a verb made from the word "cerebrum", and as Michael said, it sounds facetious. Why not use a more obvious word?

While I have heard and read this word before when studying for the GRE, it is certainly not common. It is one of the many esoteric words in the English language and is more commonly found in Scrabble games or poetry than in everyday conversation. Cerebral, which is more commonly used, has the same Latin origins. Some other synonyms include cogitate (also esoteric), meditate (common), and muse (common).

Many thanks for all the answers! It's very helpful. I'll use more obvious words. I look at a lot of websides to search for interesting topics to learn languages. So I found this strange word "cerebrate". Now I know that it isn't common in English, so I can forget it. :-) Thank you!