Long duration spells and -% Res on swap

Admittedly, even I haven't looked specifically into the druid skills in that regard as I simply never liked the ele style personally.

Generally speaking, skills inherit their direct properties at the time of casting. E.g. if you BO at say level 45 in your buff gear and then switch to dps gear which would have you at 39 or whatever, your current BO doesn't get lowered but you keep the 45 you buffed with until it expires.
Similarly, when you cast say a

Shadow Master with high-skill gear and then take that gear off, the existing traps or

Shadow Master don't get weaker.
Neither do things like

Enchant.
Base buffs or units remember their at-cast properties.

Beyond that it can (but doesn't have to) get more complicated as certain skills run extra checks upon each "sub-execution" such as

Enchant checking your current %firedmg on each attack to calculate the final, double-tapped damage or

Shadow Master checking the assassin's current skill level on each skill use to combine with the master's own at-time-of-summon level to get the final level for use.

In your case, it should be quite easy to test to make sure as things like

Armageddon tend to scale quite significantly with gear.
1) take off all gear
2) buff with

Armageddon (NEW

Armageddon, do not just re-cast over a currently running one)
3) go out and hit some random non-fire-immune mob a few times to see how much dmg it does
4) put gear back on
5) buff with

Armageddon after letting the previous one expire fully (i.e. NEW again)
6) hit same mob a few more times, observe probably very easy to spot significantly higher damage
7) re-cast

Armageddon to refresh duration (for the sake of making it more relaxed, doesn't have to be a new cast this time, refresh is fine)
8) take off your gear
9) go hit the same mob with it once again

At step 9 you will either observe the same damage you saw in step 6 in which case the damage properties are confirmed remembered from time-of-cast or you will see the same damage as in step 3 which would tell you the properties are not remembered at-cast but checked per hit instead. Get enough hits in to be sure you know what you're looking at.
Make sure it is the same mob (type) so you don't have to worry much about phys vs. fire impact. Neither part can be blocked and the spread isn't all too high on

Armageddon so that makes it easier to test. Just make sure you're looking at the actual impact damage each time and not the smaller ticks from over-time damage.
There is a slight possibility that you'd actually end up observing something in between the two damage extremes instead which..probably won't happen so let's not go too much into that for now but if it does, there's a few possible explanations for that which would simply warrant further, more extensive/targeted testing.

(The "NEW" part in the

Armageddon buffing can be quite important so keep that in mind for testing..I'll save you the explanation of why for now, adds unnecessary complexity)