Bad wires on car battery, 93 Ford Escort?

Have had trouble starting 93 Ford Escort. Some days no start, some days it starts fine, and some days it eventually goes with a pump or two on the gas pedal. First off, is pumping gas pedal like that safe to do? Why does that sometimes work? Should it work?

Even when car is running okay, it doesn't seem as strong as it did a few weeks ago (when everything was fine). Also, I noticed that when car is in idle (engine on, in park), engine sounds like it's going to kill out and is inconsistent, though not necessarily shaky. But, if I just put it into drive right away (keeping foot on brake), engine quietly roars back up to a more steady idling. For example: at a red light, everything is fine; putting into park at bank drive thru, not a good idea.

Not much of car guy. Changed air filter, thinking maybe the gas to oxygen ratio was off because of dirty air filter, but that didn't really change anything I don't think.

Looked at battery to clean connections (per advice from my father), but before I got to that, I noticed that there are two small wires that are disconnected and/or broken. I have to assume they are part of or somehow related to the larger battery cables. The two wires are right next to each other, one same side of battery. One ends in yellow plastic cylindrical female cap/tube, and the other ends in blue plastic elliptical cap/tube, with noticeable fraying/brokenness of inner metal wiring. I don't think they fit together, partially because of the shape difference (circlular vs elliptical), and partially because i didn't try to hard (i'm not totally sure what will or won't zap me).

If I need to buy new battery cables/wires, no problem, I can do that, and get help installing them from a friend if I need it. I think battery is okay. Car seems to start better when weather is warmer and dry, and not as good when cooler and moist. When it doesn't start up, it doesn't even turn over. The key gets turned and the instrument panel lights up fine, but no fire. All electrical components work fine (except A/C, which is old, and I don't really care about that).