Games26

1. Don't every play hard carries in pub. Ever.
2. If you're in a stack, remember 1 thing: Watch the map. If there is enemy missing, farm safely, ask your support to pull the lane back. Carry a Town Portal Scroll at all time. 135g is ~3 last hits, and it'll save your life, or you could Town Portal to farm in another lane.
3. Adjust your item build. Enemy team facerushing you as an Anti-Mage? Turn that Ring of Health into a Vanguard, build a Vladmir's Offering and Power Treads, go fight. Can't farm anymore as a Phantom Assassin? Turn that 3k gold into a Skull Basher/Black King Bar, go face them head on. Ganked a few times as Faceless Void/Spectre? Forget Battle Fury/Radiance, get cost efficient items like Phase Boots, Drum of Endurance, Maelstrom for Spectre, or Power Treads, Mask of Madness, Maelstrom, Crystalys, Armlet of Mordiggian for Faceless Void.

Early on in lane, a Stout Shield can be a great way to reduce incoming damage on a melee carry. I know that wasn't directly your question, but I think it's worth pointing out since taking lane harass is one of the bigger difficulties melee heroes face.

After I've used my spells and the right-click contest has begun, what else do I do in a team fight as a carry?
Using Luna in the late game as an example, I typically do something like this:

1. Poke with Lucent Beam while I wait for initiation
2. When someone initiates, run in then Black King Bar and Manta Style and right click the closest non-tank until enemy creep wave is gone.
3. Use ultimate and keep right clicking while standing still.
4. If I get low, try to run away and most likely die anyway. If enemy tries to run, Lucent Beam them to stop them.

I guess my problem is that I feel like I need to do the most DPS so I can't position myself like a support and I die fairly quickly as a result even if I have more farm than the enemy carry. Should I back up earlier while I still have life to get away and Black King Bar is still on, and then come back when they switch targets?

Bonus question:

If we're defending T3 and a teammate gets drawn out of high ground, I should probably just let them die and try our best to defend 4v5. However, what if the rest of my team runs into that lost fight? Is it better to stay alive and try to defend 1v5 or get a couple of kills and hope our barracks can survive against 3 enemies?