1.What figs need to be pollinated by the wasp? Smyrna aka caducous figs need pollination to ripen figs, they don't make any brebas ever since there is no pollen available when brebas are receptive to pollination. San Pedro types ripen brebas without pollination but need pollination for their main crop to ripen. Common aka persistent figs do not need pollination to ripen figs but some drop their breba crops usually. Caprifigs can be any of the types but since there is only pollen in the first crop that means the summer crop is the only one that gets pollinated, but the stimulation by the wasp when she lays her eggs will make the early and late crops develop to maturity... as well as the next generation of wasps.
2. And do any of the figs on my growing list (besides the unknowns) need to be pollenated by the wasp? No, most varieties that are readily available in the US are persistent.
3. Do I need a caprifig? Nope.
4. And if someone does know, how does the fig grow if it's not pollinated by a capri fig? The specific term is called parthenocarpy and it just means that the fruit is seedless, although there are seed shells sometimes they are hollow and have no embryo. When the fig wasp lays her eggs in caprifigs that is called stimulative parthenocarpy. https://en.wikipedia.org/wiki/Parthenocarpy