Arm and disarm delay in Smart Things

It’s not related to Action Tiles, but you definitely can set it to arm/disarm through a Virtual Switch using action tiles. Here’s a little write up on how to create virtual switches and use them in Intruder Alerts, it’s written for using with STHM but the same switch can be triggered by ActionTiles as well, you can use just one or two switches depending on how many states you want).

Yes it does, it’s a stand alone security system app which can work with the new and the Classic app. Check out the first post on that topic for a list of features it offers.

Keypad is any device which is compatible with the SmartThings lock standard + some additional features. Currently on the ZigBee keypad provides all those functionalities (you could even use a regular zwave or zigbee lock for that matter) but I don’t think Action Tiles provides that interface today.