What Size Wire for a Central Air Conditioner?

Size the wire to the unit's nameplate MCA (minimum circuit ampacity), not to the tonnage. The MCA is the minimum conductor ampacity the manufacturer requires, and it already includes the 125% factor for the largest motor (NEC 440.4, 440.32/440.33). Pick the smallest conductor whose 75C ampacity is at least the MCA. As a rough guide, a 2-3 ton unit runs an MCA around 15-25A, so #10 copper is common; a 4-5 ton unit can push the MCA to 25-40A and need #8 copper. Always read the data plate: two same-tonnage units can have different MCAs.

MCA sizes the wire; MOCP sizes the breaker. MCA (minimum circuit ampacity) is the smallest conductor ampacity allowed. MOCP (maximum overcurrent protective device, sometimes 'max fuse/breaker') is the largest breaker or fuse permitted, and you use a standard size at or below it. They are usually different numbers, and that is normal for AC: the breaker is intentionally larger than the wire's ampacity to let the compressor start (NEC 440 allows this because the MOCP protects the equipment, not just the wire).

No, not reliably. Tonnage is cooling capacity, not electrical load, and two 3-ton units from different brands or SEER ratings can have noticeably different MCAs. The tonnage-based ranges you see online are rough starting points only. The nameplate MCA and MOCP are the code-required values, and an inspector sizes to them, so read the data plate on the condenser.

Use a standard breaker at or below the nameplate MOCP (maximum overcurrent protection). If the MOCP is 35A and 35A is a standard size, use 35A; if the MOCP is a non-standard number, drop to the next standard size below it. Typical central AC MOCPs run 25-45A for 2-4 ton units. Never exceed the MOCP: it is the manufacturer's listed maximum.

Yes to both. A central AC or heat pump condenser must be on its own dedicated branch circuit (NEC 440.6/440.31), and a disconnecting means must be installed within sight of and readily accessible to the unit (NEC 440.14), which is the fused or non-fused pull-out box next to the condenser.