The three words are all used between two words which are similar, like the "and" in English. But their emphasises are not different.
"而且" generally have the meaning of "go forward one by one", it emphasize the words or sentences which follow it. e.g. 贝克汉姆不仅帅而且球踢得好（Beckham is not only handsome but also passed the ball well.） The sentence emphasize Beckham play football well.
"并且" emphasize the relation between the two words or between two sentences is paralleling. "并且" has the meaning of "go forward one by one", but i think "并且" is not intensitier than "而且" .
"及其" are two words. "及" is "以及", "以及" means "and", "as well as". "其" means its/his/her/their(他的、他们的等等). The its/his/her/their refer to the man/woman/something previous "及其". E.G. 他及其我（The sentence is wrong）妈妈及其女儿（The senterce is right. The daughter is mother’s daughter.）
I do not know if the explaination can help you. And i am not a professional. If there are errors, thanks to point out.