First off, my deepest condolences for you and your supervisor in this difficult time (seriously, fuck cancer). I recently went through a similar transition, albeit under circumstances that are not as tragic as yours: I'm about a third of the way through my phd program and at the start of the summer my PI abruptly decided to leave the university (and the field, so things like working with her remotely or relying on her for references/advising are also off the table). My department has been very supportive throughout the process (making sure I don't "fall through the cracks"), and I'm sure yours will be as well. In response to your more specific questions, though:
I think the good news (and it's important to focus on the positives throughout the transition) is that if you are currently writing your thesis up and preparing to defend then you already have a good idea of what you need to do to graduate. This is a positive because you don't need your new adviser to completely direct your research, you just need someone to offer feedback and invest some of their time and attention towards your project to make sure your thesis is sound and your defense goes smoothly. Even without complete overlap with the research interests of another faculty in the department, you should be able to find a faculty member that is willing and able to take the time before your defense to actually read your work and be able to appreciate it academically (which is more than enough prep to serve as your chair). Your department head/grad chair should be able to give you some guidance on this if you don't already have someone in mind.
You should also take full advantage of the mentors you have outside of your department. While they might not be able to serve as your chair, they can probably be on your committee. I'm sure they would also be more than happy to take a larger mentoring role given the circumstances (such as actually reading/offering edits on your thesis).
This will depend on the specifics of the funding (that the department head probably has at least an idea of), but in the case of my former PI, some of her grant funds were able to be accessed by the department to continue funding students for the summer after she left. I was lucky enough to have secured outside funding that started just as she left, but two other students from our lab are currently being funded using the money she left behind. If your current supervisor's funds can't be used in this way, the department may be able to fund you directly; you should not be timid about asking your department chair to explore all the possible options to fund you the rest of the way.
If your current supervisor is willing, you might consider getting him to write you a reference letter now. My former PI gave me a "generic" reference letter before she left with her permission to use it for anything that I needed it for. If not that, your supervisor can provide a reference letter about you to your new supervisor or department head and they can use to write you a letter. Either way, you should be able to get a reference for the work that you've done while in your department.