Each goddess only has one quest. Latex is always alchemists and latex cubes, rope is always a giant animated rope, metal is always robots etc. They don't apply any bindings by default, but with Bound Crusader they'll pick 2-3 random restraints that are associated with that god (it's listed in the item descriptions).
You're overthinking weapon selection, just find any melee weapon that deals decent damage for a reasonable SP cost. Swords are the most efficient overall and spears have the most OP gimmick, but as long as you're not meleeing people with a bow or something you'll generally be fine. Unarmed is a last resort.
Don't worry about losing rep for killing enemies, if a faction starts out hostile they're probably going to stay that way.
Armor does reduce damage somewhat, but the real benefit is that each piece protects you against one binding attempt. All torso armor has some kind of downside, but skirts, pauldrons and leather gloves/boots are free. Yes it looks goofy, that's why there's a setting to hide your armor.
All attacks are dodgeable as long as you have room to maneuver. Pay attention to the warning boxes.
There is a pretty decent in-game tutorial, if you weren't aware. It's the leftmost portal in the starting area.
By drones, are you talking about the Ancient Guardians drones or the Nevermere drones? The ancient drones can be drawn out and picked off like any other enemy. Wolf drones are summons, meaning your main priority should be to snipe the summoner. If they summon too many, just run away until they start despawning. (That being said, it's usually easier to just avoid starting any fights with Nevermere in the first place.)
Your main income streams come from defeating enemies and selling their dropped loot, ransoming enemies gets you almost nothing and intentionally getting tied up is terribly inefficient (the items are usually locked). You don't really need to buy more than two or three lockpicks from the shop, you can get plenty just by looting the random shiny spots on the ground.