When playing C3C I normally find a couple of bugs in the game:

The first one is one with some units' sounds: the cavalry doesn't shoot when attacking, and the Rifleman shoots while it runs (which is quite annoying, especially when an enemy starts moving tons of them through my territory, making an awful noise)

Then the one that annoys me the most is that sometimes my deals become eternal, and so I might be selling a good for a ridiculous price (for example: Iron for 1gpt, which might have been good enough in the ancient times, but not in the modern ages)

Is there a way to eliminate those bugs, especially the endless deals bug?

You have to manually cancel the deal. Just wait for the 20 turns to be over and then do diplomacy with that civ and click on "Active" which should be right next to "New" and then click on the deal you want to cancel. Make sure the 20 turns is up otherwise you will get a reputation hit.

You can also in the Preferences check "Always Automatically Renegotiate Deals" (or whatever it's called) and then every time a deal expires that civ will will contact you asking you to continue the deal or telling you they don't want the deal anymore.

The "endless deals" bug isn't a bug. It's actually a feature so that you don't have to keep renegotiating. There is, however, a preference (go to the preferences screen - ctrl-p I think) to activate it. (you need to click the circle when you're done, not enter).

For bug reports, post them in the Bug Reports thread, not here.

For the cavs without sounds bug, make sure it's not a scenario, and upload the save along with the version (i.e., C3C 1.22) that you're playing on.