is peregrine drake suitable budget replacement for palinchron in this deck?

For sure. That and Great Whale are great budget swaps.

okay im very new so sorry about this but how is Riku of Two Reflections + Palinchron: Infinite mana infinite mana if u have to keep paying mana

It's due to how you stack the triggers.
Have Riku out
-Cast palinchron
-Palichron enters battlefield
-Two triggers enter the stack (palinchron and rikus copy creature ability)
-Stack so palichron happens first then rikus.
-Untap 7 lands then resolve rikus ability tapping two lands for ability, 5 for pool.
-Copy enters the battlefield and triggers palinchron ability untaps 7 lands.
-Pay 4 Mana to return real palinchron to hand. Rinse, repeat

So you gain a net of 1 Mana each cycle and can do it infinitely if no one stops you, while also getting infinite palinchrons

Thoughts on Mirage Mirror?

Mirage Mirror would be phenomenal for him if it entered the battlefield. Since it does not, I don't think it really fits here because I'll then rely on someone else to play something worth copying and can't abuse it with Riku. I'll throw it in though and test it out to see if it's better than I'm thinking. The card is a monster in my Sakashima the Impostor clone tribal deck though :)