It could be either one. The clicking sound you hear is coming from the starter. It could be because the starter motor is weak. It worked when the extra amps from the jump start were applied. Or it could just be the cables. Give the cables a good cleaning and make sure all the connections are tight. If all works well after a few days then you have fixed the problem.
Neither is right. Have the alternator tested for a bad diode. Remove the large red wire from the alternator, if it sparks when touching the terminal the alternator is causing the battery to go dead. Be careful the wire will have current in it so watch that the wrench does not hit ground.
Sounds like an electrical issue, but it's not an electrical issue with the starter. Bad starters don't cause clocks to stop working.
Your step dad is right.
I just bought a new battery the other day. When I started the car this morning it made a click sound and wouldn't start. The time in the car was off which made me think the battery wasn't working right. I took it to the mechanic who installed the battery. The mechanic said the battery was okay and the car needed a new starter. An hour later when I was running errands the car wouldn't start. It didn't even make a clicking sound this time. My stepdad came out to clean off the battery connectors and jump start it. The car started and I was able to drive it home. My stepdad said he will clean off the battery connectors more this weekend. Was the mechanic right or my stepdad? If it needed a new starter would the car have started when the battery was jumped?