If I cast Epic Experiment and one of the revealed cards has split second , how will it interact with the other cards I revealed as I decide what to cast?
You choose the order in which you cast them, so you can cast those without split second first. After you've cast one with split second, you're done; you can't cast anything else while a spell with split second is on the stack.
But can you cast the spell, let it resolve, and then cast the other spells?
Or does the spell allow you to cast a sorcery when the stack is not empty?
(It has to be one or the other, or you can't cast more than one sorcery)
You must cast them duringExperiment's resolution; there's no waiting. You may cast any number of Instants and/or Sorceries: timing is forgotten for that while.
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of course you can cast more than one sorcery Epic Experiment allows you to
you cast the spells during the resolution of Epic Experiment, you generally can't cast spells there, but Epic Experiment allows you to, regardless of usual timing restrictions
now, if there is an additional restriction such as Split Second or a mandatory additional cost you can't pay (say Fling without any creatures on the field) that will still apply
(It has to be one or the other, or you can't cast more than one sorcery)
The only limits on which spells can be cast are those mentioned in the instructions allowing you to cast a spell*. There's nothing inherent to sorcery cards that restricts them to being cast when the stack is empty.
"Sorcery timing" is merely a limit in which spell priority allows you to cast.
Priority gives the option to the player to cast an instant spell.
Priority gives the option to the player to cast an noninstant spell if it's his main phase and the stack is empty.
On the other hand,
Epic Experiment gives the option to the player to cast certain cards.
Notice that Epic Experiment doesn't impose any conditions based on spell type, so you can indeed cast noninstants even if the stack isn't empty.
(By the way, if you were right, you wouldn't be able to cast any sorcery spells at all using Epic Experiment because Epic Experiment itself is on the stack when it resolves.)
* — Unless a replacement overrides the rules, as usual.
