So basically statpoints like strength & dexterity buff your character by itself which is shown in the character attribute window on the left. (so your skills working with that attribute are getting stronger)
Health/Mana stolen on HIT (all properties with on hit effects) only work with auto HITS, except the skill you are using says different but that's not the normal case.
Conveys X dmg over Y seconds works (i THINK) with every skill that damages foes, since the skill obtains it's damage from your weapons. you can test that pretty easily.
On strike effects don't trigger on skills but as well except the skill is saying different.
I did some testing lately and it seems that properties (unlike the DPS) are put together when dualwhielding and using skills that can trigger the effects of your left hand weapon. For example the Conveys X dmg over Y second affix does work on either hand.
No, unless it says different as mentioned before
since the weapons rotate when attacking the effects of your main hand occur on strike with your main hand and the other way around. i think "execute" (attacking with both at the same time) triggers both main and left hand weapon effects (again, Str/dex etc. are always present)
Yes it does. Simply because it buffs your Weapon DPS (look at your main hand DPS in arcane statistics when changing gear), which leads to a more powerful skill if it is using DPS (im not sure about weapon dmg thou but it should be more powerful as well). It does not power up your flat dmg skills.
I can't tell to be honest since I played vanilla long time ago and never get to lvl 100 just because it was not promising enough. Thus i didn't deal with statistics and affix tests.
If you like Shattering glaive and want to have high damage or even want to reach damage cap you actually should use dual whield (it can be dual claw/sword etc. as well, since auto hitting is really tough in end game dungeons using pistols). It is more powerful because you are able to enchant and socket 12 items instead of 11, in addition many one hand weapons have power stats like %crit and %critdmg, which is necessary for outlander depending on your gear. Shattering Glaive relies on flat damage, that being said the skill doesn't need high DPS weapons but good properties.
If you are interested in end game outlander builds check this one out. It is made by "GreatName" (Forum nickname). His youtube channel "Critical Hits Media" contains many other videos concerning Synergies Mod. https://www.youtube.com/watch?v=GPmR2uMkaDo