Can someone explain to me why they did these?

Noob in watching American football / NFL games.

https://www.youtube.com/watch?v=tKbHMfHV-zw

0:38 - 1:37:

• Why do Patriots intentionally take penalties? One of the commentators mentioned that they want to give the punter additional room. But I don't understand it - can't the punter just kick with a little less power to avoid a touchback?
• Why do Jets decline? I assume this is to counter what Patriots is doing in the above.

Same question for the next segment in the same video (1:41 - 3:32).

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