It sure is

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It sure is
How does copy effect works? I've read somewhere that Izzet Guildmage, Desperate Ritual, and Lava Spike is an infinite combo, but having Stunt Double enters the battlefield as a copy of a just finished suspension Knight of Sursi doesn't gain haste.
Copying spells on the stack works differently from copying permanents or cards in, so please don’t conflate the two. Spells on the stack are dynamic things, so copying them copies the choices made for them. Permanents and cards in other zones are more static things and thus copying them just copies them as printed (barring other copy effects).
When you copy a spell on the stack, you copy all choices made for that spell, including which alternate or additional costs were paid to cast it, which cards were spliced onto it, what its targets are, etc. This is why effects that copy spells always have to specify that you can change targets for the copies since they would be targeting the same targets otherwise.
(The combo you describe works as follows and requires 3RRR: First cast Lava Spike and splice Desperate Ritual onto it. This costs 1RR. Next copy the spell with Izzet Guildmage’s 2R ability. When the copy resolves, your opponent takes 3 damage and you get RRR. Spend that RRR to activate Izzet Guildmage again. Repeat until your opponents are dead.)
When you copy a permanent, you copy that card as it’s printed. If other copy effects apply to that permanent, you copy those effects as well. This is because copy effects happen at the lowest layer. Effects that grant abilities or otherwise change things about the card such as its color or P/T aren’t considered when copying it because they apply in later layers.
I've a few questions regarding Izzet Guildmage. They are connected, so I hope you don't mind me asking them all at once. When I play a Spell (e.g. "Mizzium Mortars") for its alternate cost its CMC doesn't change, am I right? Will the copy be overloaded? What about "Fall of the Titans", played with Surge and X=5; can I copy it?
The copy has the same choices made for it, so you can copy an overloaded Mizzium Mortars with the 2R ability of Izzet Guildmage and the copy will be overloaded as well.
Fall of the Titans cast with X=5 has a CMC of 11 (5+5+R), so it’s too expensive to copy with Izzet Guildmage.
Izzet Guildmage vs Echo Mage
Alright so I have a R/U deck going on that utilizes cheap burn spells and Scry to get to my Magus of the Future. Kiln Fiends and Wee Dragonauts are my offensive creatures, the others are around to Scry for what I need (Augury Owl, Cryptic Annelid) and to bring sorceries or instants back from my graveyard (Anarchist, Mnemonic Wall).
I was thinking that an Izzet Guildmage would be a possibility since it only costs 2 mana and it allows me to replicate sorceries or instants if I tap the mana for it. It doesn't hurt for me to re-use a Lightning Bolt again, and then have my Kiln Fiend swing for 7 power.
My roommate says that the Echo Mage is just a better version of this creature, and for the most part it is. The one thing I would say is that you don't need to tap the Izzet Guildmage to use its ability and that it would be easier for me to cast it, compared to the 2 Islands I'd require for the Echo Mage.
Thoughts? If you'd like to know more details about the deck I'm using, ask! I could use some advice from people who know more about this than I do.