you can find more info on the UCSC site and forum .
narrowpeaks can be generally called for TF, since the region bound is pretty much limited. broadpeaks are better for histone modifications or histone modifiers since the regions can be much wider. I'm not totally sure about gapped peaks but looks like you can used them when combiing regions that contain gaps (yeah, intuitive...).
and yes, you can use them for downstream analysis.
why would you want to merge them tho? that can give you gigantic peaks with basically no information. if you look at the co-binding of multiple TFs or histone marks, then I'd go for overlaps.