Who could advise me if there is any time limit between three parts of SCEA? e.g. passed Part I, any deadline to have to take Part II and Part III as well?
You can start Part II anytime you want after you've completed part I. You will have 1 year to complete Part II (from date of assignment purchase/download). Part III should then be scheduled immediately after you have uploaded/submitted your Part II assignment. Assignment grading will not commence unless you've completed part III also. (Parts II and III will be merged for grading)
But with SCEA 5 on the horizon (and the old SCEA nearing its End of Life), I wonder how that will change the deadlines?