That melee elephants don't profit from melee upgrades does not help, either.

Use masses of ranged units, preferably ranged cavalry. Once the blob of Spartan death comes close, simply run away until you're at the safe distance. Nothing worse than dealing with annoying hit and run attacks, trust me.  Keep up with the upgrades as Spartiates have a lot of base armor.

i don't know, but attack take the bonus forge

Spartain Hoplites are a bit overtuned at the moment. Swordsmen should be a cost-effective counter to spearmen, but due to the Spartain Hoplites haveing an 11% faster rate of fire it makes them already almost as good. And with then either the +10% health or the +10% damage upgrade they become a cost-effective counter to their counter.  So the default strategy is to not fight them head-on, but to build lots of defenses, destroy their Rams with cavalry and / or swordsmen, raid them, and eventually win a battle of attrition. If your Civ has access to them you can try Elephants, but then they can do the strategy to avoid them and raid your economy instead.

Can it be that the health bonus and damage bonus of promotions are calculated differently? It seems for the elite promotion the health bonus is HP*1.25*1.25 while the damage bonus is Damage*(1.1+1.1). Or to phrase it differently, health bonus affects the current HP, while the damage bonus affects the base damage.