Q1: Hold alt down over eruption and you will see what affect eruption 
Q2: Because, you have the molten shield tag that convert shield throws base physical damage to fire, it have changed the tag on shield throw, and it now states fire. And yes, fire% increased now affect shield throw. You do not need to convert shiled throws dmg, to make eruption get affected by %increase fire dmg. Eruption, should be seens as a seperate skill, and affected by different things than shield throw.
Q3: Any converted dmg, only convert the base dmg of the skill, and what you can take in the passive tree. Any sources outside of the skill, does not get converted.
Throwing attacks, does not work with Echoe.
Q4: Well it’s a difficult question. The best way i can describe it is, that you need to balance your stats out.
If you look at stats as values, they should look like 3x3x3x3 and no 1x1x1x8. Haha i dont know if that makes sense.
Q5: Well the reason why, is because as i stated in Q4, you need to balances your stats out. Increase % damage, is a very easy stat to get. And you can get it from many sources, thats why you in general, does not scale it on gear. But take what you can get from passives, and support skills.
Q6: Depends on what route you going to take. Shield throw can be build in two ways. the Throwing damage, and spell version, where you use eruption and smite.
(a): Problably the strongest option. what i have been playing myself. i love it. This type of build, also get affected by weaopen, since staff/wands increase eruptions damge.
(b): You do not need to take molten shield, if you choose to make the eruption build.
(c): This is an option to. But requires better gear. Since most of you damage, will come from the flat damage, you can get on items.
Lastly: I would like to reccomend my damage guide. Damage guide for beginners (completed) - HolyCoffee, a lot of your questions above, is better answered in my guide