You must be able to target a spell to cast Render Silent.

The affected player can still activate abilities, including abilities of cards in their hand (such as bloodrush abilities), and the player can still play lands.

If the spell is an illegal target when Render Silent tries to resolve (because it’s been countered by another spell, for example), Render Silent won’t resolve and none of its effects will happen.

Render Silent doesn’t stop any player from casting spells in response to Render Silent before it resolves.

A spell that “can’t be countered” is a legal target for Render Silent. The spell won’t be countered when Render Silent resolves, but that spell’s controller won’t be able to cast spells for the rest of the turn.