You need to read the licenses, and follow their particular terms. For some, it's as easy as just including a copyright notice and not saying "written with help of the bioPython folks!"
If you are not comfortable understanding and following a two-paragraph license, YOU NEED A LAWYER. No one else is allowed to tell you that you performing a sequence of specific steps is or is not legal. There are simply too many complexities to trust anyone without malpractice insurance and a reputation behind what they say.
(Or, of course, you could get specific permission from the copyright holder. Which is harder than you'd think for an open source project. There's a reason the FSF asks contributors to actually assign them copyright.)
That said, in general, if you make a copy of someone else's code, in whole or in part or just by using it as a guide to write your own, you can't do anything with that code without the someone else's permission. That's what licenses are for; they're written permission with some defined conditions.
If you include someone else's source code or binaries, you cannot give or sell your application to anyone, even once, without that permission. And depending on how deeply you used their libraries, you might not even be able to send the code you wrote yourself without getting their permission.
(There is a fuzzy line between "I copied their source code" and "I did only what was needed to be compatible." There are lawsuits over this all the @#$@ing time But those involve lawyers, and big budgets, and corporate liability shields.)
Thankfully, Python itself and bioPython and even Microsoft and the FSF have available libraries that have absurdly sensible redistribution terms. Even if your code is legally a derivative work, you can almost certainly license just your code via MIT, and bundle it with an installer that either has permission to include thier libraries or just points to where the user can get them from the source.
