The way crystals are formed is they are first created in a very microscopic size, which is called nucleation, and then they grow. If they grow in the middle of the same material it is called"homogeneous nucleation". However, the case you are asking about is different: here a sugar crystal grows starting from a stick or more generally a crystal of some material is growing on the surface of another material or on a piece of dirt swimming along which acts as a "nucleation point". The term for that is "heterogeneous nucleation". Both come from the Greek prefixes ομο and έτερο which mean same and different/opposite.

It's important to remember that nucleation doesn't always lead to growth: because of the fluctuating motion of the sugar molecules in and out of the new-born crystal (the nucleus) sometimes even if it initially grows a little, it can reach a critical size after which it will either grow really well and become a large, macroscopic sugar candy, or it will decrease in size and eventually disappear. But with putting a lot of sugar (increasing the concentration) you can increase collisions and make your candy edible-size and then cool it down so the molecules don't move anymore.

"Focal point" sounds like a perfectly reasonable (and universally understandable) term to me. If you want to find the "best" scientific-sounding term, some relevant fields of study to look into are crystallization and nucleation (although I believe a nucleus refers to the first grain of crystal that forms).

It's called a nucleus. The process is called nucleation.

I would call it a nucleus, or a nucleation point, or a nucleation center. This is the centre where things grow from, or in science, we would say it's the point from where they nucleate.