Plague halts all regen as well as causing a loss of hp(as damage), mana and moves on every tick. I can't tell you what exactly determines how much mana or movement you'll lose each tick, but I imagine they correlate to your Wis/Int and Con respectively.

Poison halts regen of HP and causes damage every tick for the duration.

Resist poison and disease directly mitigate damage taken from Poison and Plague respectively. In this case the effect is a known amount; 33% which can be seen via the SCORE DAMAGE command, should you have either resistance.

There are a bunch of different bleeding affects. Some do huge damage every tick, some do very little. All bleeding damage can be mitigated via the use of slow and various transmuter repair spells (some will specifically cure certain bleeding affects).

Slow and Metabolic Slowing will each boost regeneration rates across the board, for health, mana and movement. Exactly how much is deliberately obscure, but it's a very noticably effect. To be clear, plague definitely trumps slow, but I am less sure about poison.

I can't really answer your question regarding the Thick Veined edge sorry. I imagine it's a very useful amount for those characters which cannot access slowing affects for whatever reason, however.