Exiling a spell or ability prevents that spell or ability from resolving, but it doesn’t technically “counter” anything. This means that Time Stop can exile spells and abilities that “can’t be countered.”

Unless Time Stop is cast during the Ending phase, any “at the beginning of the end step"-triggered abilities don’t get the chance to trigger on the turn Time Stop is cast. These abilities will trigger at the beginning of the next end step.

Ending the turn this way means the following things happen in order: 1) All spells and abilities on the stack are exiled. This includes Time Stop, though it will continue to resolve. It also includes spells and abilities that can’t be countered. 2) All attacking and blocking creatures are removed from combat. 3) State-based actions are checked. No player gets priority, and no triggered abilities are put onto the stack. 4) The current phase and/or step ends. The game skips straight to the cleanup step. The cleanup step happens in its entirety.

If any triggered abilities do trigger during this process, they’re put onto the stack during the cleanup step. If this happens, players will have a chance to cast spells and activate abilities, then there will be another cleanup step before the turn finally ends.