Is it possible to write a universal loop program for if-then & loop programs and it is possible to write a universal while program for while progra
For part (a), there are (at least) two approaches:


Outline a LOOP program which simulates a given IF program. Seems pretty messy.
IF programs can be simulated by a WHILE program, i.e. they are recursive. Moreover, the running time of such a simulator is very manageable. A recursive function with a primitive recursive bound on the running time is primitive recursive, and so implementable as a LOOP program.


For part (b), there are again two approaches (leading to the same result):


Suppose that you had a universal LOOP program. Try running the argument used to prove that the halting problem is undecidable, and see what you get.
The running time of every LOOP program is on some level of the primitive recursive hierarchy, and the latter is strict and has infinitely many levels. Consider the running time of a universal LOOP program and see what happens.


Part (c) is about universal Turing machines.