Fire: Nonmagical fire (including alchemist's fire) does not burn underwater. Spells or spell-like effects with the fire descriptor are ineffective underwater unless the caster makes a caster level check (DC 20 + spell level). If the check succeeds, the spell creates a bubble of steam instead of its usual fiery effect, but otherwise the spell works as described. A supernatural fire effect is ineffective underwater unless its description states otherwise. The surface of a body of water blocks line of effect for any fire spell. If the caster has made the caster level check to make the fire spell usable underwater, the surface still blocks the spell's line of effect.
Spellcasting Underwater: Casting spells while submerged can be difficult for those who cannot breathe underwater. A creature that cannot breathe water must make a concentration check (DC 15 + spell level) to cast a spell underwater (this is in addition to the caster level check to successfully cast a fire spell underwater). Creatures that can breathe water are unaffected and can cast spells normally. Some spells might function differently underwater, subject to GM discretion.
For flame jet, make a DC 23 caster level check for it to work. I see no specific rules dealing with using gravity control while underwater, but your GM may add additional restrictions. The Aquatic Adventures book further clarifies that the fire spell needs to either be all-fire or all-steam, meaning you could not use it to propel yourself from underwater to being in midair, although you could use it to reach the surface of the water: "A fire spell must be either entirely steam or entirely fire, which means that if it covers an area that would normally extend beyond the water’s surface, you must choose whether to affect the region above the water or below, and the surface blocks line of effect for the rest of the spell."
Jet-based or explosion-based propulsion from Flame Jet would still logically work underwater. Gravity Control would obviously still work. You might reduce the distance slightly because water is a denser medium than air, but otherwise it should be fine.