How to fill old downspout drains
For the second question you might apply some septic dye into the old pipes. But often things get into the basement any old way, and then get trapped in the sump pit, rather than entering via the sump pit.

If you have a cleanout you can look into, septic dye might also address the assumption  that they connect to the sanitary sewer line at all. Perfectly common (but also not to be assumed without checking) that they just go out to drywells in the yard.

If they do connect to the sanitary sewer, you need to be careful not to plug the sanitary sewer if you are plugging the pipes. Inserting an expandable "test plug" to seal the pipe is a reversible means by itself, or can be a way to make sure that concrete does not go down the pipe too far and plug up what it should not. A balloon is a cheaper method for the latter, though one should put only a small quantity (2" or so) of concrete on it at first, and apply more concrete after the first section has hardened, so that excessive force is not applied to the balloon.