Summon monster spells normally last for a maximum 1 round per caster level but the summon monster spell-like ability of the summoner class lasts for 1 minute per class level.
Summoned creatures will vanish before that duration expires if the spell is dismissed (a standard action on the caster's part), dispelled or otherwise negated (there are specialized spells and abilities that dismiss conjured creatures) or when the summoned creature drops to 0 hp or is killed. Summoned creatures are completely obedient to their summoner (unless someone seizes control over them through magic) and will fight to death if there will be such need.
Eidolon is separate case. Once summoned it stays summoned until dismissed, banished or killed. Th sole exception to this is when the summoner, instead of using 1 minute ritual (10 rounds) to summon the eidolon, conjures it using 2nd level summon eidolon spell, which has duration limited to 1 minute/level.
Note that eidolon summoning ritual is too slow to be efficiently used in battle as fights often end before 10th round. However, except for social disadvantage of walking around with clearly magical companion, there is little that would prevent summoner from walking around with eidolon summoned all the time.
One minute in battle equals 10 rounds?
Yes; one round is 6 seconds.
One minute in battle equals 10 rounds?Yes; one round is 6 seconds.
Approximately 6 seconds