Unfortunately a lot of caldarius’s strengths are only brought out by reps, so you should really enjoy playing him if you want to use him effectively. Getting used to jumping as a background constant and managing your cooldowns so you can effectively escape are crucial. While playing him you should rarely stop jumping, and absolutely never stop moving. If you’re adept with him he can ably go toe-to-toe with any character in the game; he excels at both dueling and harassing because of his mobility, high burst, and good sustained damage, while also being an excellent waveclear with his good aoe damage, lifesteal, and minion-cc effects.
So I want to clarify up-front that yes, though he’s good at finishing fleeing opponents, there is absolutely no reason to relegate yourself to only fighting low health enemies. You should be shooting, blinding, and generally being an overbearing nuisance to everyone you see (with the possible exception of boldur who is basically impossible to kill unless he stays in lane too long or you have help).
That said, I’m not sure his role changes too much between modes, frankly. I like to flank with him to gank either lone enemies or groups of weak ones in meltdown, but that isn’t really as possible in incursion (the flanking part). His blind seems to be more useful in incursion as an initiation tool, where you blind a group of enemies before moving in as a unit or use it to disrupt a dive/push; the skill’s large aoe and the long blind duration post level 4 make it ideal for singling out supports while the enemy team flounders around unable to see or help.
Gear-wise, my favorite build consists of a zero-cost health regen item with negative recharge rate (you should never need to leave lane with regen so you can farm quickly; the flaw turns out not to be a big deal, and it allows you to buy this next item very early), a sportsman’s max health item (for its cost this is the strongest health item in the game, and will help you survive stuns long enough to escape or get your cooldowns back), and lenore’s lament (stat stick that also gives his tmp lifesteal, in effect giving you ~30 health per second while fighting non-jennerits including minions). For non-legendary situations like tournaments I run a skill damage+max health instead of lenore’s, simply because it increases his burst and health is the strongest stat in the game atm.
Stats that are less useful but still viable are attack speed, cooldown, and d.r.+health regen, but I would very strongly recommend you not run move speed or anything similar, simply because you’ll be jumping so much that they should rarely come in handy.
I guess lastly to address your question about his melee, I think it mostly comes from experience when the time is right (or if you should just patiently wait for your reload rather than get yourself killed trying to melee someone). That’s obviously a non-answer, so I’d say as a general rule I like to go after supports like ambra, alani, and miko throughout the game with it, but it’s useful to tag anyone with it who relies on strong regen when they’re not looking or when you’re certain you can win a fight. Jumping in close for a single melee and jumping away to continue tmp-ing will not only handicap an opponent’s regen but will also keep them unsure about what range to engage you in. Generally don’t try to stand there a melee someone to death, if you’re going to use your blade then there’s no reason to not keep jumping around your target aiming for crits.
also helices: right right middle left right right left right left left
and I’ve said too much. so. good luck. he really isn’t ■■■■ I promise.