coilprotectionrelaytransistors
In the circuit the relay is controlled from a manual switch on a 12v bus. I can't understand why you would want to add the extra components of the transistor and diodes to the circuit? ie why are D4, R1, T1, D1 needed? Thinking about cost and component count here.
To select a switching transistor, you'll need to know how much current will flow through your 12V LED. Choose an NPN transistor that can pass that current, allowing a good margin of safety. You're looking for the Ic(max) parameter in a data sheet.
From a quick look at the relay board I note the following:
These components provide for a buffered drive circuit of the relay coil. The below schematic is the likely configuration of these components. (LEDs not included).
You should be able to connect your 5V supply between the VCC and GND inputs. Then connect the GPIO signal to the IN1 terminal and also the MCU board ground to the GND pin.
This driver circuit should work with either a 0->3.3V swing or 0->5V swing GPIO. Not knowing just how those two LEDs are connected up it may be that one or the other LED may not work with a 0->3.3V swing of the LEDs are connected into the base circuit of the transistor. On the other hand if the two LEDs are connected up into the collector side of the transistor similar to as follows the the LEDs should work as well. A simple check of the circuit with an ohm meter should be able to confirm how the LEDs are connected.
Best Answer
The transistor and the resistor might be needed because the input can not supply enough current to drive the relay. D4 protects the transistor from a negative voltage at the input.
D6 protects the transistor from a negative power, and prevents spikes to enter the power rails.
A relay that is switched off produces a current pulse that must be dissipated somewhere, otherwise it will destroy the transistor. D1 could be intended to protects the transistor against this pulse, but IMO it is placed wrong: the diode should be in parallel with the relay coil.
I can't see any purpose for D3, unless it has something to to with components connected to the vertical wire that are not shown.
All in all this looks like a circuit produced by a committee with too much open agenda's and some closed ones too.