You are correct, the EVAP valve should open once at startup and then shut off. Unless there is some problem with the ECU or a chaffed wire I can't come up with a reason for it to behave differently. The Green wire to the valve should have battery voltage any time the car is on. The Blue/Green wire goes to the ECU. The ECU takes that wire to ground when it wants the valve to open. If the insulation on the Blue/Green wire got scraped I suppose it could cause the valve to keep randomly operating.

There is really no correlation between the EVAP and the remote. It could be that the batteries in your remote are getting weak. The Guard series alarm system is rare in the US, most of the cars here came with just the basic alarm system, and I really have no experience with it.

Your codes are a knock sensor code and a long term fuel trim code. Try to clear them and see what comes back. The fuel trim code is often just a dirty MAF (AMM) sensor. Just spray its element with some electrical contact cleaner and let it dry. Don't scrub it or even tough it - it is very sensitive.

...Lee