Do not use the "on-board" relay to switch mains voltage. The board's layout does not offer sufficient isolation between the relay contacts and the low-voltage components. If you want to switch mains voltage - mount the relay somewhere safe - Away From The Board.
The relay is energized by pressing a single key. Choose the key you want to use - and connect it to terminal "E". Choose the four keys you want to use to de-energize the relay - and connect them to "A B C & D". Wire the common to R1 and all the remaining keys to "F".
The Circuit is easy to use. When you press "E" - current through D2 & R9 turns Q6 on - and energizes the relay. The two transistors - Q5 & Q6 - form a "Complementary Latch". So - when you release the key - the relay will remain energized.
To de-energize the relay - you need to press keys "A B C & D" in the right order. When you do so - pin 10 of the IC goes high - and it turns Q4 on through R8. Q4 connects the base of Q6 to ground. This unlatches the complementary pair - and the relay drops out.
Any keys not wired to "A B C D & E" are connected to the base of Q3 by R7. Whenever one of these "Wrong" keys is pressed - Q3 takes pin 1 low and the code entry sequence fails. If "C" or "D" is pressed out of sequence - Q1 or Q2 will also take pin 1 low - with the same result. If you make a mistake while entering the code - simply start again.
The Keypad must be the kind with a common terminal and a separate connection for each key. On a 12-key pad, look for 13 terminals. The matrix type with 7 or 8 terminals will NOT do. With a 12-key pad - over 10 000 different codes are available. If you need a more secure code - use a bigger keypad with more "Wrong" keys wired to "F". A 16-key pad gives over 40 000 different codes.