(3) Your build is good, although building armor items kind of depends on your opponent, so that's something to keep open. (2) I can also say your Cannon Barrage upgrades are in order, as Fire At Will! makes it a lot more of a threat. Death's Daughter and Raise Morale are bought at your own discretion. (4) Considering that his Parrrley procs Dead Man's Plate, and that Trial By Fire and Powder Keg give movement speed boosts, it would be relatively ideal to buy Dead Man's Plate - smack someone with your Passive or bust a keg, run around in a circle for a moment, and discharge the Momentum stacks into some poor individual. Plus the Armor, Health, and Movement Speed is nice. (1) Against Melee Champions, use your barrel as a threat. Drop it in the middle of an area, somewhere plainly visible, and keep relatively close to it - close enough that you'll be able to break it before they will. Setting up for damage is rather difficult, as you need to be able to estimate how you'll link your barrels up. If I'm in pursuit, I usually throw a barrel ahead of the target - this will either slow them down as they try to break it before I do, or they'll pass close enough to it that I can Parrrley it and slow them considerably. Or, you can alternatively set up a barrel in a hidden location, such as a bush or beyond the Fog of War, and then try to chain up barrels when your opportunity strikes. Or, if you're confident and maxed out your Powder Kegs, set up a minefield. It gets fun.
EDIT: As for possible alternative builds - try buying Tanky items with a mix of damage - like Maw of Malmortius, Mercurial Scimitar, Frozen Mallet, Black Cleaver, etc. Having the health and damage mix does tend to put things in your favor, and Black Cleaver's CDR and armor cleaving makes damage a lot easier and allows for quicker use of your Remove Scurvy.