In what order prerequisites will be made by the GNU make?

Sure, if I use make -j a, they might all get built at the same time (depending on whether b, c, d, or e in turn have other/interrelated dependencies).

No, the order is not defined. That is the whole point in using declarative dependency-oriented programming: that the computer can pick the optimal evaluation order, or in fact, evaluate them even at the same time.

In the right order, based on the rules you provide. For your particular example, that could mean any one of a number of different (4! = 24, from memory) orders.

All make programs are free to choose the order they like as long as the dependencies are honored. If there were other rules in your example, say c: b, then c would be made before b (but that isn't the case, as you point out).

If you need to rely on a specific order, you'll need more rules to enforce it. Otherwise make can do what it pleases. The documentation for GNU Make only states how rules are processed, not the order in which dependencies within a rule are processed. The most logical order (to me, anyway) would be the order in which they're listed but that's not guaranteed.

In what order prerequisites will be made by the GNU make?

It depends on the type of the prerequisite. According tho the GNU Make Manual, Section 4.2:

There are actually two different types of prerequisites understood by GNU make: normal prerequisites such as described in the previous section, and order-only prerequisites. A normal prerequisite makes two statements: first, it imposes an order in which recipes will be invoked: the recipes for all prerequisites of a target will be completed before the recipe for the target is run. Second, it imposes a dependency relationship: if any prerequisite is newer than the target, then the target is considered out-of-date and must be rebuilt.

Normally, this is exactly what you want: if a target’s prerequisite is updated, then the target should also be updated.

Occasionally, however, you have a situation where you want to impose a specific ordering on the rules to be invoked without forcing the target to be updated if one of those rules is executed. In that case, you want to define order-only prerequisites. Order-only prerequisites can be specified by placing a pipe symbol (|) in the prerequisites list: any prerequisites to the left of the pipe symbol are normal; any prerequisites to the right are order-only:

   targets: normal-prerequisites | order-only-prerequisites

The normal prerequisites section may of course be empty. Also, you may still declare multiple lines of prerequisites for the same target: they are appended appropriately (normal prerequisites are appended to the list of normal prerequisites; order-only prerequisites are appended to the list of order-only prerequisites). Note that if you declare the same file to be both a normal and an order-only prerequisite, the normal prerequisite takes precedence (since they have a strict superset of the behavior of an order-only prerequisite).

Consider an example where your targets are to be placed in a separate directory, and that directory might not exist before make is run. In this situation, you want the directory to be created before any targets are placed into it but, because the timestamps on directories change whenever a file is added, removed, or renamed, we certainly don’t want to rebuild all the targets whenever the directory’s timestamp changes. One way to manage this is with order-only prerequisites: make the directory an order-only prerequisite on all the targets:

OBJDIR := objdir
OBJS := $(addprefix $(OBJDIR)/,foo.o bar.o baz.o)

$(OBJDIR)/%.o : %.c
    $(COMPILE.c) $(OUTPUT_OPTION) $<

all: $(OBJS)

$(OBJS): | $(OBJDIR)

$(OBJDIR):
    mkdir $(OBJDIR)

Now the rule to create the ‘objdir’ directory will be run, if needed, before any ‘.o’ is built, but no ‘.o’ will be built because the ‘objdir’ directory timestamp changed.