Hello, Azz and Ahmed—In my opinion, only (b) and (d), the "up to now" sentences, are grammatically correct; sentences (a) and (c) are not.
"Up to now" is similar to but differs in usage from "until now," the latter indicating that a situation has remained constant until now.
We could indeed say both "I have received applications until now" and "I have received applications up to now" with near semantic equivalence.
However, when we quantify the number of applications received, only "up to now" works, whether it is placed at the beginning or at the end.
The reason is that the receiving of four applications is not something that can continue throughout time, at least without a subinterval specification, e.g.:
a'. Until now I have received four applications a day.
c'. From last Tuesday until now, I have received four applications a day.
The situation of receiving four applications a day is something that can continue throughout time, until or up to now.
If I have received four applications since last Tuesday, then it is true that, up to now (i.e., so far), I have received that number of applications.
If I have received four applications since last Tuesday, it is NOT true that I have received four applications ever since then!
But that's what "until now" indicates.