Open the faucet served by the frozen line so melting water has somewhere to go, then warm the pipe gradually starting at the faucet end and working back toward the frozen section. Use a hair dryer, heat gun on low, heating pad, or space heater in the room. Never use an open flame. Stay with the pipe while it thaws, because a split line will start releasing water the moment ice clears.
The clearest sign is a faucet that produces no water or only a trickle during cold weather while other fixtures work normally. Other indicators are visible frost or condensation on an exposed pipe, a bulged or deformed section, gurgling or banging when you open the tap, and unusual sewer odor from a drain whose water seal has frozen.
No. Many frozen pipes thaw without failing. Failure happens when expanding ice traps water between the ice plug and a closed faucet, and pressure in that trapped section rises until the pipe wall or a joint gives way. Rigid copper and galvanized steel split more readily than PEX, which can expand somewhat. Damage often appears during thaw, not while the pipe is frozen.