<p>Many of your questions involving amount of time taken, workload, and courses during graduate study are rather specific to the subject, and can vary considerably from student to student. Course work is usually done early in the graduate program, and many graduate level courses are places where faculty recruit graduate students to research projects.</p>
<p>PhD students may pick up a master’s degree along the way, as a master’s degree may involve course work, or course work plus a master’s thesis (typically much “smaller” than a PhD thesis). At PhD granting schools, some departments only accept graduate students initially intending to do PhD degrees, though not all complete the PhD. Others do accept graduate students initially intending to graduate at the master’s level (this is more likely in more obviously pre-professional subjects like engineering). Again, there is a lot of “it depends”.</p>
<p>Math may be a subject where the 1.5 year PhD is more likely to occur – there are some extremely brilliant mathematicians around, so if one of them proves a major theorem not long after entering graduate school, that may result in his/her PhD without having to do a lot of time consuming lab or field work. It may be different for a plant biologist studying the growth of bristlecone pines.</p>