Superwario - I answered part of your question in your other thread. (in regards to the factory remote not working while remotely started)
As for your other issues:
Key Takeover - The only company that has a data solution for the CX-5 is ADS. In their first solution, you could allow key takeover where you unlock the door, hop in, and then drive away (similar to what Tundraroamer explained) this early solution also required you to permanently lose a key for the remote start to activate. With their newer update, you don't lose a key for the remote start to work, but as a security/liability issue they can't offer key take over. If the car would not shut off when the door is opened, essentially a thief could break in and drive away with your car while it is remotely started. It has no way of knowing that you are getting in with the key.
Light flash - This came down to a lazy install by your installer. Wiring into the parking lights on the CX-5 is a pain in the butt, but it is do-able. The lazy alternative is to wire into the hazard switch to give you a visual confirmation of the remote start's operation. The downside? The lights will flash the entire time the car is remotely started.
As for your other issues:
Key Takeover - The only company that has a data solution for the CX-5 is ADS. In their first solution, you could allow key takeover where you unlock the door, hop in, and then drive away (similar to what Tundraroamer explained) this early solution also required you to permanently lose a key for the remote start to activate. With their newer update, you don't lose a key for the remote start to work, but as a security/liability issue they can't offer key take over. If the car would not shut off when the door is opened, essentially a thief could break in and drive away with your car while it is remotely started. It has no way of knowing that you are getting in with the key.
Light flash - This came down to a lazy install by your installer. Wiring into the parking lights on the CX-5 is a pain in the butt, but it is do-able. The lazy alternative is to wire into the hazard switch to give you a visual confirmation of the remote start's operation. The downside? The lights will flash the entire time the car is remotely started.