how can i explain the following? (from grammar point of view)
...but Professor K. has not yet arrived
All applicants are to fill out this form...
thank you in advance
The first example is just a different order for the common expression that you know: somebody has not done something yet.
Here are some patterns that all have this same meaning:
she has not done it yet
she has not yet done it
she has yet to do it
Your second question is an interesting one: be + to + base verb functions the same as modal + base verb, but the meaning depends on the situation.
Look at these examples:
1.A. They are to get married next week.
1.B. They will get married next week. (or They are going to...)
2.A. Applicants are to fill out the form in pen.
2.B. Applicants must fill out the form in pen.
I hope this helps.