Could is the past tense of can. These two words are among the many that form a class of MAV modal auxiliary verbs called the ‘pure’modals. AV’s (Auxiliary verbs) are helping verbs that help the main verbs to convey additional information. MAV’s are a type of AV. MAV’s help to convey shades of meaning: permission, ability, necessity, advisability, possibility, probability and so on.
Can & could convey permission as in requests and statements and general, physical and mental ability. They also convey degree of sureness (definiteness) and possibility.
Could expresses the same idea as Can except in a weaker, less direct, more polite and more formal manner.
I'll try to add modal meaning to each of your statements:
1. You could ( = are permitted to) shut up and sit down. [expressing permission]
2. You could (= might like to; =might) give me a hand with the cooking. [expressing request]
3. You could (= are permitted to; = might) phone Mary and see what time she's coming.[expressing permission/suggestion]