No, he is talking about connecting it to the rain sensor port on the OSPi board (far right connector next to stations). That connector is connected (internally) to the GPIO 14 that you show on your picture.
Yes I think both of them would work with OpenSprinkler / OpenSprinkler Pi. Most rain sensors are simply rain-activated switch — some are normally open (i.e. switch is disconnected when there is no rain) but most common ones are normally closed (i.e. switch is on when there is no rain). OpenSprinkler software allows you to choose between the two types of sensors.
I use the Hunter Industries sensor – you may need to adjust the polarity inside the config for it to work correctly but once that is done it just works.
Yes, pull-up is required because the firmware itself doesn’t enable pull-up, so it assumes there is external pull up. You can modify the firmware yourself to enable the internal pull-up.