1. Yes and No.
If a spell’s caster dies or is incapacitated during the spell’s
duration, the spell remains in effect till its duration ends.
You might need to keep track of the caster’s initiative after
they stopped being able to act to monitor spell durations.
Because all summon spells are sustained up to X amount of time, technically the summon is still around until the end of the casters next turn. They won't be able to act during that time, but they will still be present. This is important depending on the circumstances.
Say a Wizard had a summoned wolf from a previous turn. They sustain the spell then move, triggering an attack of opportunity. They are knocked out by that AoO. The wolf would still "exist" until the Wizards next turn in initiative, though it wouldn't be able to use any actions since the Wizard was not able to sustain the spell, thus "commanding" it.
...Otherwise, the summoned creature uses the standard abilities for a creature of its kind. It generally attacks your enemies to the best of its abilities. If you can communicate with it, you can attempt to command it, but the GM determines the degree to which it follows your commands. Immediately when you finish Casting the Spell, the summoned creature uses its 2 actions for that turn. Summoned creatures can be banished by various spells and effects. They are automatically banished if reduced to 0 Hit Points or if the spell that called them ends.
2. Dispel Magic would banish a Summoned Creature by ending the spell that summoned it.