I would like to know in what order the resource tabs are arranged from left to right (alphabetically by name?), and whether and how I can let CT to remember the customized order.
The order of tabs is not determined at the (re)start of the project. The cause is various loading time of the resources (e.g huge Total Recall can load longer than web resources). Also, ProZ.com resources available via API are initiated early at the start so its tab comes first. Nonetheless, there are some techniques possible to rearrange the order of the tabs which may be explored in the future. For now, the most important tabs can be docked automatically after restart or reordered manually.