Guild Wars 2

So, I have the Purity trait and Resolve for my heal. How do these 2 work together? 2 condition cleanses every 10 seconds? 2 cleanses every 20 seconds? Or do they simply not stack at all?

It wipes 2 every 10 seconds. The signet/trait are on the same timer so it will take off two at once.

The way Signet of Resolve works is that it is constantly ticking its passive effect every ten seconds regardless of whether you have a condition on you or not. That means that if you happen to take a condition at the 9.99 second mark it will cleanse it .01 seconds later.