If I use Summon Monster I, can I slap a celestial or infernal (or at higher levels of spell, other templates) on the summoning?
Look at the summoning tables again. Any creature with a star beside its name (*) already comes with either the celestial or fiendish template on it, depending on the casters alignment.
The majority of creatures you can summon already have one of those templates on it.
Other then that, you can not apply any template to a creature you summon (unless you have a special ability that lets you do so.) (The Animal Shaman druid archetypes can apply the young, advanced, and giant templates to their totem summons, for example.)
Yes, celestial or fiendish. If B2 is allowed, entropic and resolute are also allowed.
This is for Summoned Monster, though. This doesn't work for SNA though.
Creatures on Table 10–1 marked with an “*” are summoned with the celestial template, if you are good, and the fiendish template, if you are evil. If you are neutral, you may choose which template to apply to the creature. Creatures marked with an “*” always have an alignment that matches yours, regardless of their usual alignment. Summoning these creatures makes the summoning spell's type match your alignment.
In PFS, I don't think the entropic or resolute are allowed, however.