When does your phone probe? Specifically, does it stop probing after you have connected to a network?
Whenever it feels like it. This can be pretty much all the time, but in practice you won't see this happen much once the device is connected to a network and is happy about it. It's up to the implementors to decide when to send probe requests, and it varies from device to device, firmware to firmware.
When will the mac address not be randomized?
MAC address randomization isn't all that typical. See also: https://www.theregister.co.uk/2017/03/10/mac_address_randomization/
Associated with a network means connected. That is, the client sends out packets tagged with the SSID of the network it's targeted towards. Many SSIDs can share the same channel, and the channels overlap. It's necessary to indicate at the low level of the packet what network it's supposed to go to. When the client decides it's joined the network is when it is associated with that SSID.
In general, you can use MAC addresses for tracking who all has connected. Don't rely on it for anything critical though. People change devices, have several devices, sometimes forget their devices, and it's even possible to change your own MAC address when you feel like it.