Are any biology research journals free to publish in?
Many biology journals are free to publish in. As a rule of thumb:


Most journals from for-profit publishers such as Elsevier, Wiley, etc. charge nothing to the author (but of course bill the libraries handsomely).
Many but by no means all society journals charge page charges even if they are not open access.
Most but not all open access journals charge substantial publication fees. You could try this website to search for open access journals that do not charge publication fees.