Borderlands – Is it possible to trade Seraph weapons with a player that doesn’t own the Captain Scarlett DLC

You are the only one who can add to your challenges, save for one or two specific ones like the car compacter in the dust. So your friends hitting enemies you've slagged doesn't add to the bonus slag damage the challenge has said you've dealt (although it does add to your friends challeneges, since they're the ones dealing the bonus damage), and slag weapons don't deal any bonus damage, only their own damage.

As someone has said you do indeed need to switch to another weapon after slagging an enemy to deal bonus damage. It's also possible to use slag explosive barrels or, since you seem to be playing as the Siren, using the ruin or scorn skills.

I was hoping for a more authoritative answer, but after >50 hours of gameplay using mostly elemental weapons, I'm pretty darn sure there's no longer a tech pool.

Elemental guns deal consistent damage and elemental effects are randomly distributed. The visual effects are consistent (either a shot was elemental or not, you can tell by watching the bullet impacts).

This means that slow firing weapons are worse for stacking elemental status effect damage than high rate of fire weapons, which is sort of the opposite of how the old Tech Pool worked. The status effect chance % as listed appears to be the only relevant factor for "procing" a shot, though it's affected by skills, class mods and Badass bonus stats.