There are big differences between British English and American English here, so be careful! (For example, in Br English, you don't "graduate" from school; and "school" usually refers to where children go - although a university may well have 'a School of Humanities'.) This post will refer to British English.
1 'He's left school'. If he didn't do what American English would call 'graduating', you'd say 'He left school without qualifications'.
2 'I'm at college'; if you want to be more specific 'I'm studying/doing Chemical Engineering'. Nowadays (for the last 10-15 years), people have been saying 'I'm going to uni' (adopting an Australian English abbreviation [at least, I think that's where it came from], as a result of Australian-made soap operas - which are affecting not only words but also intonation]; or 'I'm at <place-name>'.
3 'I'm a graduate'; 'I have a [first] degree' ('a degree' is assumed, without an obvious post-graduate context, to be a first degree - e.g. B.A. or B.Sc.)
[none of your numbers]
3a 'I'm doing a Master's/M.A./M.Sc./M.Phil...' - This is a one or 2-year course (typically). Some establishments provide other post-graduate diplomas - often called 'a Post-Graduate Diploma' (for example, the Open University gives masters courses, but people who do only the first part - probably a large number of years of part-time study) get such a diploma.
4 'I'm doing a doctorate'.
4 [Your second one!] I don't know what sort of degree you mean; perhaps you made a cut/paste mistake. But if you're doing ''post-doctoral work' you'd call it that (or some other noun, as applicable - maybe a 'post-doctoral course'. Often, people doing post-doctoral work are called 'research assistants'; of course, that's a generic term, and anyone helping with research may be called a 'research assistant'. But research assistants are often doing post-doctoral work. Adverts at jobs.ac.uk, for example, often advertise for paid positions - 'Research Assistants' - that specify a doctorate as a job-requirement.
I hope that's not too much information; it cuts several corners already (often specific to one or a few universities - e.g. most universities have a PhD, but the equivalent degree at Oxford is called a D.Phil).
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