protostar - Is the conversion from proto-star to main sequence an event or a process?

Astronomers distinguish a prototstar from a star based on whether the object is visible. A protostar is hidden by the gas cloud that surrounds it. Protostars aren't visible. At some point in their evolution (and where this occurs depends on mass and metallicity), a protostar will start clearing the surrounding cloud of gas. This process happens very quickly from an astronomical point of view. (Aside: From a human point of view, this is anything but quickly.)

In the case of very massive stars, the newly emerged star is already on the main sequence. Very massive stars are "stars" (objects with a stable mass, stable size, and fusing hydrogen into helium) well before astronomers can see them. In contrast, very small stars spend hundreds of millions of years of evolution between being a "star" (visible to astronomers) and being on the main sequence. The star is a pre-main sequence star during this long span of time.

Intermediate mass stars also spend some time as a pre-main sequence star. How much time depends on mass and metallicity. In the case of a star with a mass of ~1 solar mass and metallicity comparable to that of the Sun, the time spent as a pre-main sequence star is on the order of tens of millions of years. In contrast, the time spent as a protostar is very short, tens of thousands of years. The time taken to clear the star system of gas (the transition from protostar to PMS star) is shorter yet, hundreds to a few thousand of years.

There is no point at which one can say fusion starts. It's a probabilistic thing, with probability increasing sharply with density and temperature. What about objects at the low end of density and temperature? This is the boundary that separates red dwarfs from brown dwarfs.

There is very little difference between the smallest red dwarfs and the largest brown dwarfs. The smallest red dwarfs are quite cool. They fuse hydrogen into helium via the p-p chain, but rather infrequently. The largest brown dwarfs also fuse hydrogen into helium via the p-p chain, but here the fusion reactions are so very infrequent that the brown dwarf gets cooler and cooler. In a trillion years, we might be able to point to a marked boundary between old red dwarfs and old brown dwarfs. Right now, that boundary is rather arbitrary.