There’s a few ways you can tackle this with various degrees of rightness.
First of all, your door looks to be hung upside down. That’s not going to affect the fit of the door but it is going to put your doorknob at an awkward height.
Your best bet is probably going to be to go get a new, pre-hung door, and replace the entire thing, frame and all. It’s really not that hard, just kind of fiddly getting everything squared up properly. You can probably get it done for less than $200, and a few hours of work with a friend or two.
Second best bet is going to be to square up the existing frame, get yourself some shims a prybar, and some nails, pull off all the trim, and set it right.
In my experience, trying to get a new door to fit right in an existing frame is always kind of a pain in the ass. It sounds like more work, but it’s usually worth it to go the pre-hung route.
There’s lots of guides and YouTube videos on how to do all of that.
Least right- start modifying the door and/or frame so they fit. Cut, plane, chisel, and/or sand the door and frame down until they fit. Yes, the door is probably hollow, but you should still have probably about an inch or so of solid framing around the perimeter of it to work with. There’s a good chance if you go this route you’re going to find it looks kind of wonky and you’re going to wish you did one of the above options.
You could always of course pay someone to do it the right way. Shouldn’t be terribly expensive, I’m a cheapskate and will DIY most things, but I have a personal dislike of installing doors, so it’s something I’d be willing to pay for.
Depending on how you can rearrange furniture, how much wall space you have next to the door, etc. you could also go with barn doors and just bypass the crooked frame entirely. I hat barn doors, I think they just look bad in pretty much all cases, but they’re popular for some reason and pretty straightforward to install.
Depending on your tastes and how much of an actual barrier you need, may also be able to get away with bifold doors, a curtain, cafe/batwing/saloon doors.
Most sump pumps, at least in my area, drain directly to the outside, there’s basically a pipe that goes from my sump up and out of my basement and opens out into my yard.
I wouldn’t really want to count on a sump pump for this kind of issue though. At best you’re basically just putting a bandaid on a sucking chest wound. You could also run into some legal issues for knowingly using it to discharge sewage into your yard (and why would you even want to do that in the first place?)
It would also be pretty rough on the pump, they’re usually not meant to handle solids like the hair clogs, bits of food, fecal matter, etc.
Assuming you’d have an actual sump pit installed, there’s often some water left standing in the pit, you probably don’t want that to be sewage water.