Your question was asking for Code references for what you already knew was wrong, there are several NEC violations represented here. First most clearly is:
NEC 210.21(B)(3) Receptacle Ratings. Where connected to a branch circuit supplying two or more receptacles or outlets, receptacle ratings shall conform to the values listed in Table 210.21(B)(3), or, where rated at higher than 50 amperes, the receptacle rating shall not be less than the branch circuit rating.
If you find that too ambiguous:
NEC 240.4(D) Small Conductors. Unless specifically permitted in 240.4(E) or (G), the overcurrent protection shall not exceed that required by 240.4(D)(1) through (D)(8) after any correction factors for ambient temperature and number of conductors have been applied.
(6) 12 AWG Copper 20 amperes
Then you were spot-on when you advised a new circuit for the fridge, receptacle outlets in the kitchen should not be shared with those in the living room. There is some room for grandfathering if it was legal when installed, but altering a circuit requires meeting current Code:
NEC 210.52(B) Small Appliances.
(1) Receptacle Outlets Served In the kitchen, pantry, breakfast room, dining room, or similar area of a dwelling unit, the two or more 20-ampere small-appliance branch circuits required by 210.11(C)(1) shall serve all wall and floor receptacle outlets covered by 210.52(A), all countertop outlets covered by 210.52(C), and receptacle outlets for refrigeration equipment.(2) No Other Outlets. The two or more small-appliance branch circuits specified in 210.52(B)(1) shall have no other outlets.