Learn French: Ce morceau est certes opaque, mais il est très tranchant. - This piece is admittedly opaque, but it is very sharp.

The lesson teaches c'est + invariable adjective for general statements or commenting on a whole situation (like saying 'that is sharp' in general). However, this sentence describes a specific, previously identified noun: ce morceau (this piece, masculine). When referring back to a specific noun, you must use the pronoun that matches its gender and number (il est or elle est).

What is the exact role of certes in this sentence?

Certes means 'admittedly', 'to be sure', or 'certainly'. It is a classic B2-level adverb used to concede a point before introducing a counter-argument. You will very often see it paired with mais (but) later in the sentence to express: 'Admittedly [A], but [B]'.

Can I use tranchant to translate 'sharp' in all contexts, like a sharp pain or a sharp mind?

Generally, no. Tranchant comes from the verb trancher (to slice) and is strictly used for physical objects with a cutting edge, like a blade or a jagged piece of glass. For a sharp pain, you would use aigu, and for a sharp or quick mind, you would use vif.

Why doesn't the adjective opaque look like a masculine adjective to match morceau?

It is in the masculine form! The default, base spelling of opaque simply happens to end in an 'e'. In French, any adjective whose masculine singular form already ends in an unaccented 'e' remains exactly the same in the feminine singular. It only changes when adding an 's' for the plural.