If you cast Primal Surge and you put Purphoros, God of the Forge as your fourth creature entering this way, will the previous three creatures trigger Purphoros?
Also, how does Purphoros interact with other devotion gods? Do they need to have their required devotion when entering to trigger Purphoros (i.e. 5+ devotion for mono; 7+ for multi)?
On your first question: No. With Primal Surge, you put permanent cards onto the battlefield one at a time, not simultaneously. By the time you put Purphoros onto the battlefield, it won't see any previous creature enter the battlefield, even one that you put there with Primal Surge. (Compare with Collected Company.) However, its third ability will trigger if you put a future creature onto the battlefield with Primal Surge.
On your second question: For Purphoros's third ability to trigger, the permanent must be a creature "under your control" at the time it enters the battlefield (so that for permanents that are normally creatures and have an ability of the form "As long as your devotion ... is less ..., [this permanent] isn't a creature", "your devotion" of the stated kind must be equal to or greater than the stated number at the time that permanent enters the battlefield, taking into account that permanent and any other permanent entering at the same time as it) (C.R. 603.6a-b; review C.R. 700.5). If the permanent isn't a creature at the time it enters the battlefield, Purphoros's third ability won't trigger for that permanent even if it becomes a creature later. Note that the God creature type (C.R. 205.3m) has no abilities or game mechanics inherent to that type, including the mechanic where the permanent in question is a creature or not depending on its controller's devotion.
As for Purphoros's last ability, it checks which permanents "you control" are creatures at the time it resolves and gives only those creatures +1/+0 until end of turn (even if they cease and resume being creatures in the meantime) (C.R. 611.2c). Other permanents won't get +1/+0 this way even if they come under "your control" as creatures during the turn (C.R. 611.2c). This is because the +1/+0 effect is from a resolving ability and changes the characteristics (here, power and toughness [C.R. 109.3]) of certain creatures (C.R. 611.2c).
Also, how does Purphoros interact with other devotion gods? Do they need to have their required devotion when entering to trigger Purphoros (i.e. 5+ devotion for mono; 7+ for multi)?
On your second question: For Purphoros's third ability to trigger, the permanent must be a creature "under your control" at the time it enters the battlefield (so that for permanents that are normally creatures and have an ability of the form "As long as your devotion ... is less ..., [this permanent] isn't a creature", "your devotion" of the stated kind must be equal to or greater than the stated number at the time that permanent enters the battlefield, taking into account that permanent and any other permanent entering at the same time as it) (C.R. 603.6a-b; review C.R. 700.5). If the permanent isn't a creature at the time it enters the battlefield, Purphoros's third ability won't trigger for that permanent even if it becomes a creature later. Note that the God creature type (C.R. 205.3m) has no abilities or game mechanics inherent to that type, including the mechanic where the permanent in question is a creature or not depending on its controller's devotion.
As for Purphoros's last ability, it checks which permanents "you control" are creatures at the time it resolves and gives only those creatures +1/+0 until end of turn (even if they cease and resume being creatures in the meantime) (C.R. 611.2c). Other permanents won't get +1/+0 this way even if they come under "your control" as creatures during the turn (C.R. 611.2c). This is because the +1/+0 effect is from a resolving ability and changes the characteristics (here, power and toughness [C.R. 109.3]) of certain creatures (C.R. 611.2c).
EDIT (Feb. 5): Add comparison.
EDIT (Mar. 13): Edited.