Yes to all the above. But take
canis root and imp stool, or imp stool and swamp fungal, and you got a potion that can paralyze someone while you beat on them.
Blue mountain flower and blisterwort for restoring health
creep cluster and red mountain flower for restoring magicka
histcarp and purple mountain flower for restoring stamina
nirnroot and chaurus egg for invisibility
blisterwort and glowing mushroom for fortifying smithing
falmer ear and river betty for damage health
jazby graqes and skeever tail for ravage health
deathbell and salt pile for slowing someone down
blue dartwing and orange dartwing for fortifying pickpocket
In the list above, only the nirnroot really has to be purchased, as the rest can be easily found anywhere in Skyrim. At first one will get low numbers, but as you raise your alchemy level, you will be surprised what you can get. I only use 3 points in alchemist, with physican and benefactor. Later on, when my alchemy gets way up there, I will add poisoner, concentrated poison and green thumb.
The best part about alchemy, besides gathering ingredients, and making potions, is that it is free to get ingredients except for the nirnroot. Basically, alchemy cost nothing but some perks and gathering.