Use of relay 5V instead of 3.3V
use a LDO or DC-DC converter to give you 3.3V for the MSP430 and the sensor. The LEDs will also be powered from this, using a series resistors to drop 1.1V. Chose the value of resistor to give you the LED current and brightness that you require.
Rather than use a 5V relay, why not use a 9V relay from the same manufacturer? Then you can power the relay directly from the battery. The 5V relay cannot be guaranteed to operate correctly from 3.3V since it has a Max Operate Voltage of 3.75V. If you must use a 5V relay then you will need a separate LDO or DC-DC to give you 5V.


The relay current is, as you say, Voltage / Coil resistance.

There are 3 versions of this relay, specified as the power consumption of the coil, ie 0.15W, 0.2W, and 0.36W. If you use the most sensitive (0.15W), and use the 9V version, then the current required is 16mA. A PP3 will be able to supply this current, but not for very long.