Could someone explain the main differences(mainly on how the signal or stream is sent)?

How do cable companies get the original feed from all their channels?

Does weather effect the feed with Direct TV more than Dish Network? Will we ever see the day in which weather won't play a part in their broadcasts?

Sound quality? Which is better Cable or Satellite?

Cable is by cable, land lines essentially. Satellite is by Satellite, so signal. Streaming is via internet.... however you get that from the source to your TV. That's the most basic to put it.

How does Cable tv get the feed from ESPN. Satellite?

It was C-Band satellite in the 80s, don't know how they do it now.

I've had more experience with DirecTV than Dish. My parents were customers when I was a kid and I later got it at my previous apartment and now at my current home. Sometimes in lighter snow or rain storms, the feed doesn't get effected. My aunt and uncle have Dish and I housesit for them about ten times a year. There was a heavy snow storm that took out the feed. Some people I've known have claimed that their satellite signals are never effected by bad weather.