You can safely have up to 4 potion effects active at once (including healing potions). 5 makes you take slight damage, but not quite enough to overtake a healing potion. 6 is more serious and 7+ is rather lethal. Now, you will have to make more decisions as to which potion is most valuable for a specific fight.
All poisons are much less potent, but last for many more uses. Treat them more like weapon oils in Witcher. Paralyze, frenzy and fear are now chance based to proc. Poison effects stack, but remember that Weakness to X poisons bottom out at -100% weakness.
Alchemy no longer makes any money. This coupled with the merchant gold change is intended to eliminate Alchemy as being such an overpowered source of income. NPCs arbitrarily overvalue certain effects, pay more for potions with bad side effects, and for some reason trust this dubiously skilled drifter to make reliable and quality potions for which they are willing to put their store’s reputation on the line to sell. And that’s assuming that you aren’t just lying about the effects of the hundreds of random potions you create. Only reputable alchemists should realistically deserve the right to sell potions to Skyrim’s people.
Healing Poultice now heals a flat amount of health instead of regeneration. However it is probably the cheapest and most efficient non-restoration way to heal out of combat, and is very plentiful at alchemists. You will also commonly find them on bandits.
Skooma now works like Jet/Turbo from Fallout instead of giving you giant stat buffs + a random chance to die or get paralyzed. It also causes addiction, which confers significant regeneration penalties when you're not skooming. It also provides slow time as an extra boost against regenerating enemies if you don't quite have the DPS yet. You can cure skooma addiction by taking an Alchemy perk that allows you to make a cure, or you can take the Restoration perk Painful Regrets (which is a one-time reset on crimes and skooma addiction).
Fortify unarmed damage added as a new alchemical effect, and can be found on vampire dust, large antlers, powdered mammoth tusk, ashen grass pod, and bear hearts
Vampire dust can no longer give you vampirism. You'll need to head to a cooking pot and mix together the appropriate ingredients for a guaranteed way to get vampirism
Requires 1 elixir of blood and 5 vampire dust. Elixirs of blood can be found on vampires, with strong vampires having a high or guaranteed chance.
Damage stamina regeneration poison changed to Vulnerability, which lowers enemy armor rating.
Damage magicka regeneration poison changed to Impairment, which lowers enemy attack damage.
Wards and shields prevent poisons from being applied.
Replaced one of the Fortify Light Armor potion with Resist Projectiles, which lowers incoming bow/crossbow damage.
Constitution (resist poison) alchemy effects now also lowers stamina cost to attack by 1/4 of the poison resistance magnitude.
Healing poultices restore 1/5 of the normal health gain while in combat. This will keep your health bar up instead of fading, which is nice.
New poisons introduced to replace the following vanilla poisons: damage magicka, damage stamina, lingering damage magicka, lingering damage stamina, ravage stamina, and ravage magicka. In their place are poisons that deal fire, frost, shock, magic, and sun damage, and a poison that causes the target to be vulnerable to soul trapping. They do damage over time.
For these to work effectively, you need to go into the mod Scrambled Bugs settings file, and find the line "Poison Resistance (default: disabled)". Enable it, and enjoy.
There are no pre-made potions in vanilla skyrim/requiem for ravage stamina/magicka, so the only way to access soul trap and sun damage poisons are by crafting via alchemy.
It's worth noting that these poisons will bypass traditional immunity to poison resistances and work on things like dwemer automatons. To make sense why this would happen, they're called "oils".
All alchemy effects previously with these effects are simply changed to have the new effect in its place; some ingredients may be worth looking at now when they previously weren't. In general, there are 4 tiers of strength for the new poisons.
Holding Thunder's heart boosts your alchemy level