Should I power up my Charizard?

I would power it up. Such a crazy pokémon and not useless, but Arcanine its much better so only do it if you have lots of dust. This move will be ok against Lapras and Exeggs. Mine comes with Ember/Dragon Claw ¬¬.

Atack set is good to power it up. If you have dust and candy, You can use them for it. It won't dissapoint you.

If you like using it, go ahead. But Wing Attack is better against grass types since it does more DPS and it's lower cooldown also means it's going to lose less DPS through dodging. Plus fire + flying typing has double resistance to grass.

Unlike flying type moves, fire does extra damage to ice and steel, although currently the only steel type is magnemite/ton, and Charizard's flying type negates the effectiveness of fire's resistance to ice unlike Arcanine, which has resistance to ice due to it's pure fire typing, so you end up doing neutral damage to Lapras due to it's water typing, meaning Wing Attack would still be better, and you end up taking neutral damage. There are better neutral pokemon, but since gym battling is so easy anyway it's basically just use what you think looks cool.