No. The composing typically releases something like 30% of the C to achieve a stable C:N ratio of ~12:1. And the compost itself degrades quickly under average soil conditions.

Indirectly.

Compost itself is not a carbon sink. But when you apply it to the soil, compost increases the humus content of the soil which, in turn, is a carbon sink.

How dos this work?

In the process of composting, the organic matter of the raw materials has 3 destinations : a part is released as CO2, a second part is converted to slowly biodegradable organic compounds, and a third fraction is converted to humus precursors. When the compost is integrated in the soil, these humus precursors wil be further transformed to final humus compounds. (Those remain there, hopefully, for centuries.)

I think partially you can say as composting stores more carbon in the soil than it emits to the air , but as Prof. Paul mentioned compost itself degrade quickly which is very valid point. We know a sink is a reduction in atmospheric GHGs by storing (sequestering) carbon in another form. A traditional carbon sink is actually the underground coal and oil deposits where millions of year ago living plants (and other organisms) used atmospheric carbon.