q1. both work the same. the larger device may be inconvenient because of its size.
q2. 22 is 22 ohms. 1/2 Watt is fine. Other common values around 22 like 18, 27, 33 will work too. If you go too small (say, 10 ohms or less) it defeats the purpose of installing a limiter in the first place. If you go too high (like 47 or more) it may limit the voltage available to activate the coil. See below.
GRJ's schematic shows a single-diode to convert the AC to DC. This is call half-wave conversion since the diode only transfers one half of the AC waveform. If you use a bridge-rectifier or full-wave conversion you transfer both halves of the AC waveform. The math gets nerdy and depends on capacitor value, relay coil resistance, blah, blah, blah. The bottom line is using a bridge-rectifier may apply too much voltage (power) to your 12V DC relays and overheat them.
Some off-the-shelf relay modules as shown earlier include electronics to limit the power to the relay. Others simply specify the range of allowable track voltage thereby limiting the power in the relay. If you want an "engineered" design, provide a link to the relay datasheet and range of track voltage over which you operate.
