The answer would be normally no. As described in the rules about magical fire underwater. If the caster has made a Spellcraft check to make the fire spell usable underwater, the surface still blocks the spell's line of effect.
No. Magic does what it says. A lightning bolt or fireball do exactly what it says despite your thoughts of water changing them, because its magical fire & lightning, not mundane. Rules state though a creature FULLY submerged in water has fire resistance.
Produce Flame does what it says it does — it sits in your hand and produces light, or you can throw it to do damage, ending the spell. Being underwater does what it says — if the creature you throw the flame at is fully immersed, they have resistance to the damage.
Crossbows, nets, javelins, spears, tridents, and darts are able to be used normally underwater. For all ranged weapons, even those that aren't subject to disadvantage, they must be used within the weapon's normal range. Going beyond that, the attack automatically misses.
In addition to this, any ranged weapon attack must be within the weapon's normal range otherwise it automatically misses. This means that a heavy crossbow can only be shot within 100 ft. underwater even though it has a maximum range of 400 ft.
A bright streak flashes from your pointing finger to a point you choose within range and then blossoms with a low roar into an explosion of flame. Each creature in a 20-foot-radius sphere centered on that point must make a Dexterity saving throw.
These magical flames can't be extinguished through nonmagical means. Since water is non-magical, an Immolated target should burn quite nicely underwater. (For up to 1 minute, if you concentrate, and they fail their save.) And just a reminder, in 5e a character cannot chose to fail a save voluntarily.
None of the spells you list, nor any spell you can cast, would be affected by being underwater except for the resistance creatures acquire against fire. Creatures and Objects that are fully immersed in water have resistance to fire damage.
Thermite, a mixture of rust and aluminum. YouTube/TheBackyardScientist This flowerpot full of red powder looks pretty innocuous. But when ignited with a strip of magnesium and a blowtorch, it yields a molten metal so hot it keeps burning underwater.
The spell Arcane Eye states: You create an invisible, magical eye within range that hovers in the air for the duration. Since spells do what they say they do and nothing else, the Arcane Eye would not be hovering nor in the air, so therefore cannot be used underwater.
Fireball deals unusually high damage for its spell level, hitting all targets within a 20-foot radius for 8d6 fire damage (an average of 28 damage per creature). The Dungeon Master's Guide suggests that 3rd-level spells that deal damage to multiple creatures should deal 6d6 damage per creature.
If deep enough underwater, even if the target is visible, there would be no reasonable path for the projectile to take and still do damage. At lesser depths, it may slow the projectile. I'd personally treat a deep target as having total cover, giving the projectile no chance of inflicting damage.
But this is the first time we've seen underwater archery, and we're pretty amazed at how accurate a bow can be in the pool! If the temps are high where you are, and you're an archery fan, this might be the perfect way to cool off….
Special underwater communication systems have been developed to allow divers to talk to each other underwater. A transducer is attached to the diver's face mask, which converts his or her voice into an ultrasound signal.