Yes, you can change the valve that empties the black water tank. I did this on mine. Got the replacement dump valve from etrailer.com. They're not expensive and not particularly hard to replace. Your problem though, is that you have waste water (and other contents) still in your tank, if you couldn't empty it. As you remove the old valve, the contents of the tank will start leaking out around the valve fitting. I don't know what to tell you to do, except have a big bucket handy and maybe just loosen it some, until the bucket gets nearly full, then tighten it up again so you can dump the bucket in your toilet. Repeat as necessary until the contents are drained. If you have "solids" in there, this will not get them out, but maybe you can dump them once you have changed the valve. I'd lubricate the new slide with plumbers grease before you insert it.
The leak at the drain pipe connection to the black tank is also easy to fix. I repaired mine by coating the entire joint with ABS cement (bought at Home Depot), then pressing fiberglass cloth onto the still wet cemented areas and applying more ABS cement over the entire "patched" area. The fiberglass cloth makes a very strong patch and it adheres to the tank and pipe well with ABS cement. I think I repeated this process once more after the first application had dried.
There are numerous posts on these problems in the Plumbing section.
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