Aside from the rights and wrongs, if you don't work your notice your employer is entitled to keep back a proportion of your final wage.
I think you may have been given bad advice about whether you had to provide a sicknote for this latest absence. Irrespective of bad feelings, as you have had absences 3-4 months ago it was reasonable to ask for a sick note in this instance. Different firms have different arrangements for sicknotes, some needing one from the first day, others after 3 days but not for many years have I heard of a firm only wanting one after a week.
Your boss is a nasty bully and if you can manage to move then you are probably better off doing so.
Very few cases of constructive dismissal come to anything, although litigation lawyers may give you to understand otherwise. In this instance, without a carefully documented period of harassment which other colleagues were prepared to swear occurred, you are on dodgy ground.
You also need to check the probation period the firm works to, and how your hours stack up - you may not qualify for 'full time permanent' levels of job protection and could be liable to be terminated with no reason, so work out your leave and walk away is my advice.