Yes my knowledge level is not great but I’m planning on putting the new cassette on myself. (That’s why all the help is really appreciated)!

(I have two questions)
1. So what I’ve gathered here is you cannot (JUST) replace the plates cage parts, is that correct? (see pic).
2. Also can someone tell me if these will be ok/correct for a Shimano 105, 5600 group set? Or provide me correct cassette/link. - Here’s what I’m looking at but I don’t understand the numbers.
Amazon.com : Shimano XT CS-M771 Bicycle Cassette (10-Speed) : Bike Cassettes And Freewheels : Sports & Outdoors

OR

Amazon.com: Shimano HG81 10-Speed Cassette (11-34T)

Thanks a bunch guys!!