My doors don't unlock unless I press the button

The "Smart Key System" or SKS detects the FOB (the door lock remote) from about 6 ft. and when you place your hand behind the drivers door handle (on the outside) will unlock either the drivers door, or all doors (selectable). The two versions of this system worked from either the driver's door only, or from the drivers door, the front passenger door, and from the hatch door. The passenger and hatch door detection unlocks all doors.

So, does your car go into "ready" when you press "start" with the FOB in your lap and your foot on the brake? If so the FOB battery is probably ok. If you have to hold the FOB up to the "start" button the FOB battery is dead and needs to be replaced. Until the FOB has a good battery the SKS won't work.

I won't comment on the alarm part of your question except to say you want a compatible type. Ask at the dealer. Probably too expensive, but asking is free.

 

I think you need to consult a dealer and try to get an Owners manual for that model and year.

If you have a push-button key fob, chances are excellent that you DO have an alarm.

And the door handle lock/unlock requires an actual touch to operate. Likely that you do not have that feature.

After-market alarm systems often are not a good idea because they will run your battery down if the vehicle is not driven once a week or so.

 

I think it’s in the owners manual where you can set that setting to have it automatically open for you when you’re near the door handle. Maybe someone disabled that mode for your car before you bought it?