[Avodah] Questions about mechiyas amalek

[Marty Bluke via Avodah]

1. When Shaul returns to Shmuel Hanavi after fighting Amalek he says
hakimosi es dvar hashem that he destroyed Amalek and in fact, the Medrash
states that Amalek only survived because Agag was allowed to live the night
and it was his descendents that perpetuated Amalek.

However, the Navi says (Shmuel 1 30) that a few years later David fought
Amalek in Tziklag and 400 Amalekim escaped. Who were these Amalekim if
Shaul had wiped them out a few years earlier?

2. Why did no King after Shaul attempt to fulfill this Mitzva? Both David
and Shlomo certainly had the power to do so and yet they never attempted to
wipe out Amalek, nor did any other king, why not?
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