Is this worldly life a realm of reckoning and punishment from God, or a realm of tribulation, and are Muslims and non-Muslims equal in this regard?

There is no evidence to suggest that people will be held accountable in this world with an accounting that includes the tabulation of their deeds and their requital for them. The reckoning that encompasses this will take place on the Day of Judgment. As for what occurs in this world, it is part of the recompense for their deeds or a trial for them. Allah may punish the disobedient in this world for what their hands have earned, so that they may return [to Him]. He may also test the believers to raise their ranks. He may punish disbelievers, as happened to previous nations. And He may gradually draw some of them in, increasing their blessings before destroying them.