Code without an explicit license is protected by copyright and is by default All Rights Reserved. The person or people who wrote the code are protected as such. Any time you're using software you didn't write, licensing should be considered and abided.
(Brian Doll (GitHub's VP of Marketing))
So, with that taken into account:
If the code can be used in my project, am I free to then licence that code under the same as the rest of my project or even to just license the code by itself?
From Help: Open source licensing at GitHub:
It's your right not to include one with your code or project, but please be aware of the implications. Generally speaking, the absence of a license means that the default copyright laws apply. This means that you retain all rights to your source code and that nobody else may reproduce, distribute, or create derivative works from your work. This might not be what you intend.
Even if this is what you intend, if you publish your source code in a public repository on GitHub, you have accepted the Terms of Service which do allow other GitHub users some rights. Specifically, you allow others to view and fork your repository.
Thus no, you cannot license the code again. There is no relicensing of the default license. You cannot rework it into another work that you release or use to provide services to others (if you can use it in personal projects is something left to the courts and possibly de minimis, but that is something for a court to decide). You can view it and fork it in accordance with GitHub's Terms of Service.
If you were to add a license to your code at a later date, would that only affect future releases of the code? For example, if I were to fork something unlicensed and then the original author adds an all rights reserved copyright - can the forked code be used as long as it was prior to the addition of the license?
Adding a license does not make things retroactive (see If someone changes their license, does it apply to previously forked projects under the prior license?). It only applies to future versions. Note that changing from "no license" to "all rights reserved" is no change. No license is all rights reserved.