Alternative costs + cost increasing effects.

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If someone were to cast Runeflare Trap for its alternate cost while a Thalia, Guardian of thraben was out would they have to pay a Red and one colorless or only the Red? Same situation but casting any spell using Omniscience while thalia is in play. And then a final situation of using Isochron Scepter to cast something while thalia is in play.
Trap would be for its alternate cost

any non-creature spell via Omniscience would be

Isochron Scepter would cost to activate and then you'd pay to cast the copied card from exile

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Additional costs still need to be paid. To calculate the total cost of the spell, start with its mana cost or alternative cost (your examples use alternative costs), then add any additional costs, then subtract any cost reducers, then apply Trinisphere.

So for runeflare trap, the total cost = + =

For a spell cast via omniscience, the total cost = + =

For a spell cast via isochron scepter, the total cost = + = (and of course you'll need to pay , to activate the ability).
If someone were to cast Runeflare Trap for its alternate cost while a Thalia, Guardian of thraben was out would they have to pay a Red and one colorless or only the Red?


They have to pay


Same situation but casting any spell using Omniscience while thalia is in play. And then a final situation of using Isochron Scepter to cast something while thalia is in play.



Same.  You have to pay the

When determing how much to pay, First you determine the mana cost or alternate cost to cast the spell.  Then you add in any increasers and subtract any cost reducers, then apply effects like Trinisphere

In your examples, the additional cost of Thalia is added to the alternate cost of casting the spell.
 
If someone were to cast Runeflare Trap for its alternate cost while a Thalia, Guardian of thraben was out would they have to pay a Red and one colorless or only the Red? Same situation but casting any spell using Omniscience while thalia is in play. And then a final situation of using Isochron Scepter to cast something while thalia is in play.

Cost-increasing effects do apply to alternate costs like the Trap's or even "cast without paying its mana cost" (which works like an alternate cost of for the spell)


So Runeflare Trap would cost , spells cast with Omniscience cost . The Scepter's activated ability still costs just , but then you need to pay to cast the copy you created.

[<o>]
Thanks a lot everyone for the detailed responses, I thought this was the case but I always like to double check.