are the mature sperms of all animals provided with flagella?

Answer 1

Most multicellular animals have swimming sperm with flagella, although a few like the nematode worm Ascaris have lost the flagella for swimming and move by crawling. Amoeboid sperm.
http://jcs.biologists.org/cgi/content/full/115/2/367

They are all mobile even in organisms like green algae Chlamydomonas. Both gametes of these organisms usually have two flagella that serve for swimming and also as arms to grab and stick to each other for fertilization in water. http://www.uwlax.edu/biology/faculty/Howard/Research.htm