I have anxiety with tanking in every dungeon/trial until I have run it well a couple times. There are early dungeons I am still anxious about every time I run them, Dzemael comes immediately to mind.
All that works for me is more practice. Sometimes, if a dungeon has me nervous I just queue that specific dungeon like 3-4 times in a row to make sure I get a good bead on it. Nothing beats familiarity to relieve anxiety.
For speed pulling expectation, Odsvarta has the good call:
Speed pulling is a matter of how well DPS can AE, so on the first pull, get the first two packs of trash (like 6 mobs, most likely) and see how it goes. You'll know what your PUG can do and can adjust from there.