If you cast a spell off of Epic Experiment, you won’t be able to pay any alternate costs for it [such as Overloading a Mizzium Mortars, or having your opponents gain life to cast Invigorate]. The reason for that is because Experiment is having you pay an alternate cost [of not paying at all!] when you cast the spell, so you can’t choose to pay TWO alternate costs.

However, additional costs are still able [and in some cases, required] to be paid. You can kick/multikick a spell you cast with Experiment, and you can pay for Buyback as well, if you choose. And if your spell has a mandatory additional cost [like Fling or Infernal Plunge], then you MUST pay that cost in order to cast the spell. You can choose not to cast the Fling if you don’t have any creatures you’re willing to sacrifice, though.