From what I understand, doujinshi are self-published works. this means that doujinshis can be written by anybody (the original author, fans, others artists, etc) that are about the characters & story of the work. djs are usually canon when written by the original author--but there are time when original author doesn't make it canon but just play around with their characters bc they think its interesting. on the other hand, anything made by other creators relating to the work is not canon. so the answer to your last question is YES. It's possible for original author to publish their work w/o a company and tat is what a dj is.
For this doujinshi, it was made from the same mangaka of the main story and it is canon. instead of publishing with the original story, this dj was published separately.
Whats the definition of a doujinshi? I used to think it’s just a not canon manga xD but am i wrong?