Why don't you use that nice piece of flex tubing that I saw on your bed? I'm guessing it's probably cause it's pretty big. If that doesn't work you can either hard line it (which can be difficult and isn't as "flexible" in both ways lol) which you should use 45 degree bends whenever possible over 90s but yeah the best way is like Big K said and is with flex line.
Since my drain is bigger I use a piece of flex/pool vacuum hose tubing (two since I have two drain lines) like I saw on your bed for that, and then I use a barb fittings with clear flex tubing (I use the stuff that's got the braided fiber stuff in it to keep it from squishing the tube) for my return pump. In order to use the barb fitting you would just replace that thread to slip fitting you have on the return line ball value with a threaded barb fitting.
As far as the pump line goes since you said it's like 1 inch, maybe get a 1 inch threaded coupling (threaded both sides):
Then a reducing bushing:
Then finally a barb fitting to screw into that to connect your hose (same like I was saying above):
A lot of times these kind with the threads on one side are nylon, but you can find them in the plumbing section in little packages. If you want a pvc one they are usually female slip kind so you would need some pipe too, but they make nylon threaded ones that are pretty big.
wouldn't hurt to throw a union somewhere to make your pump or plumbing easy to remove and service:
I believe they make threaded ones too.
Are you using teflon tape on all those threads?
This is how I would do it but maybe Big K would know a better way since he's a plummer I mean plumber :D
Hope this helps!