The answer to your question is "it depends". The major problem is that there's no DVR software for Android that supports CableCard DRM (in fact, there's little software for any platform that does - AFAIK, the only thing that does is Windows Media Center, which is all but discontinued). SiliconDust has been saying that HDHomeRun DVR will support this eventually, but until it does, you're at your cable company's mercy as to what channels you can pull, and every cable company is different in this regard. Some companies will not DRM any channel, some of them will only DRM premiums, some of them will DRM anything that's part of an add-on package, some of them will DRM everything except local channels. It's not even consistent with a particular provider; local franchises often have their own rules.

With a cablecard all the channels should work since the cablecard should come from your cable company.

What won't work is DVR on DRM channels like most likely HBO and Showtime would mostly have.

If you're one of the lucky ones your cable company might not DRM their channels so you might be able to record.

First off, my condolences for having mediacom, I had them for years in iowa and they were the worst lol. I have a Connect as well as a Prime with Charter. (you are right you need a prime for cablecard) Like others said most likely the large majority of your channels should work with the HDHomerun android TV app or the Live channels app except premiums (for me the only channels that seem to be protected but included in my base package is Starz). The DVR should work with all those channels too with the same caveat. I wish plex DVR could be set from the app but right now (as I would guess you know) it only works on the PC web interface. Bear in mind if you're not familiar with cablecards is the cable company hates them so it's a pain in the ass to setup, and they seem to be flaky too I had to swap cards a couple times before one worked. I did mine in November this last year.

If you already have Plex setup, it works great. I usually let my computer record and process the shows. Then watch them when I get time, but the live TV in Live Channels works well. One annoying issue I ran into was that the program guide doesn't download until you open the app. So if it's been a while since you watched anything, it takes a few minutes until the guide shows what's playing. But if you already know what you want to watch, it's only a slight annoyance.

Have you thought about getting HDHomeRun for OTA for Fox/NBC/CBS etc and getting something like SlingTV (with the 5 dollar kids package extra that includes Disney Junior, Disney XD, Nick JR, Nicktoons, Boomerang (Hannabarbara stuff?), TeenNick, Sling Kids

You can add on HBO / Showtime through sling if you want.

As others have said it depends what CCI bits they have toggled on the channels. I have Comcast in the North East and can record everything but my premiums. I know TWC flags everything as record once, which gets in the way of anything that cannot support DRM. Google for CCI + your provider, something like Tivo would have the same problem so you can find their support level and go from there.