[RPG] Can you summon an Elemental Myrmidon, and if so, do you need the armor

If you break concentration it becomes hostile and might attack you

From the invisible stalker entry under Directed Hunter, "...forced to serve until the magic that binds it expires". The magic that binds it is Conjure Elemental and when you lose concentration that magic expires.

Then we go to Conjure Elemental which says, "...you lose control of the elemental, it becomes hostile...and it might attack", so that happens.

If you die it becomes hostile, and could attack you, but instead just finishes its task and leaves

In a nice case of specific beats general the invisible stalker entry says, "If the summoner dies in the interim, the invisible stalker vanishes after completing its task". So if you manage to die without first breaking concentration for another reason (say from massive damage) the invisible stalker will finish what you asked of it.

Summon Monster doesn't allow you to summon any creature of the elemental subtype, it allows you to summon the specific creature called “Elemental”. The table is a list of specific creatures, not creature subtypes:

The spell conjures one of the creatures from the 1st Level list on Table: Summon Monster.

What might be throwing you off is the links in the Summon Monster tables in the PFSRD. Unfortunately, the links are misleading. Most of PFSRD's links are automatically detected, but the generator can't tell the difference between “elemental” (the monster name) and “elemental” (the outsider subtype). Since the subtype is much more commonly what that string of letters means in the SRD, the automatic linker defaults to the page for the elemental subtype — which is the wrong meaning in this case.

In other words, when it says that Summon Monster II can summon an “Elemental (small)”, it means that you can summon a Small Fire Elemental, a Small Lightning Elemental, etc., not a small version of any creature with an elemental subtype.