My first question is if I use the "Amazing Initiative" ability to give myself one extra standard action can I combine that with a quick runner's shirt to get two full round actions in one turn? what about the mythic haste that lets you take an extra move action every round?
At 2nd tier, you gain a bonus
on initiative checks equal to your mythic tier. In addition,
as a free action on your turn, you can expend one use
of mythic power to take an additional standard action
during that turn. This additional standard action can't
be used to cast a spell. You can't gain an extra action in
this way more than once per round.
Second with the legendary item Path ability can you add a mythic spell to an intelligent item? The info about mythic spells in item's is below as well as the wording of the ability to get spell casting.
Mythic Spells in Magic Items: Mythic spells can't be crafted into magic items unless the item is an artifact (for
example, you can't brew a potion of mythic cure light wounds).
So assuming I take the Legendary item ability two (making it a minor artifact) or three times (Making it a major artifact) could I add on a mythic spell?
Spellcasting: This item allows it's bearer to cast a limited number of spells as spell like abilities. This ability can be taken moree than once. Each time it's taken, the bonded creature gains 5 points ot spend on selecting what spells it can cast. A spell costs a number of points equal to it's level (minimum one). The bearer can then activate the item to use each spell like ability once per day. By spending double the cost, the bearer can use each spell like ability three times per day. All spells must come from the same class's spell list. No spell can have a level higher than the bonded creature's tier. The caster level for these spells is equal to double the bonded creature's tier.The save DC for these spells is equal to 10+the spell level+the bonded creature's tier.
1. No. Amazing Initiative gives you an additional standard action and the quick runners shirt an additional move action. Thats all. They dont add up to a full round action. Same for mythic haste.
2. You need the ability to cast mythic spells and you need mythic power. Legendary items cannot learn this prerequisites so they cannot learn/use mythic spells.
As far as I know, there is no way to get a second full-round action on the same turn. The closest thing I can think of is some creatures' "Extra Initiative" ability, which gives you another turn entirely, or the mythic monster ability "Dual Initiative", which also gives you another turn (but using different mechanics).
As for the mythic spells from legendary items: Mythic stuff is extremely house rule. Ask you GM. For me, a reasonable compromise would require you to have Mythic Crafting, and any time you cast the spell you'd have to expend a use of mythic power to boost the SLA to mythic just as if you had cast the actual spell yourself.