Answering the last question first, there is no need for thermal reliefs for a via, unless you intend to fill it with solder. The thermals make soldering easier as heat is not drawn away as quickly from the point were you want the solder to melt. But I'm not sure that thermals are an absolute necessity; that's probably a good question for your PCB vendor.
I'm not sure there is much, if any difference between the staggered and aligned vias. Also, filling the vias or not won't make a BIG difference, but solder obviously conducts better than air. If you need to get the absolute best conductivity, then fill your vias.