I have a bunch of mana rocks, isochron scepter (imprinted with counterspell), and paradox engine in play.
I cast a spell (for argument's sake let's say it's a sol ring). Can I repeatedly use the isochron scepter to counter the sol ring and make infinite mana?
Yes. When you cast the copy of the Counterspell card with Scepter, it triggers Paradox Engine. After PE's trigger resolves, but before counterspell does, repeat it with the untapped Scepter.
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I cast a spell (for argument's sake let's say it's a sol ring). Can I repeatedly use the isochron scepter to counter the sol ring and make infinite mana?