How do 9-unit thesis courses fit into my timetable? 9 units = 3 classes, so that means I have 21 units (7 classes) to register for to maintain a full course load. Do I choose if how these classes are split between first and second term? ex. 3 in first and 4 in second.

I think you can choose but I heard from someone that the 3 units are typically done in 2 terms since you need your marks to know if you can graduate or not.

You get to choose which term to take 4 courses and which term to take 3.

I'd recommend taking 4 first semester and 3 second semester, I found the second half of the year much busier thesis-wise than the first.

I agree, I took a nine-unit thesis as well and positioned the bulk of my courses in the first term. It helps loads; you get a much more spacious last term which you need to write your thesis in.