why the for loop version use much less memory?

for (x..y) loop and for (@array) loop (but no other kind of for (LIST) loops) are optimized to iterate over the list without flattening it.

$n = 10_000_000;
print ": ";  <>;                                       # 2MB
$f = 1;
for (0..$n-1) { if ($f) { $f = 0; print ": "; <>; } }  # 2MB
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$n = 10_000_000;
print ": "; <>;                                   #   2MB
push @a, --$n while $n;
print ": ";  <>;                                  # 240MB
$f = 1;
for (@a) { if ($f) { $f = 0; print ": "; <>; } }  # 240MB
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grep { ... } LIST flattens the list, so grep { ... } @array loads the entire array* on the stack and grep { ... } 0..$#array; create a list in memory as big as the array.

$n = 10_000_000;
print ": ";  <>;                                         #   2MB
$f = 1;
grep { if ($f) { $f = 0; print ": "; <>; } 0 } 0..$n-1;  # 240MB  <--
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$n = 10_000_000;
print ": "; <>;                                     #   2MB
push @a, --$n while $n;
print ": "; <>;                                     # 240MB
$f = 1;
grep { if ($f) { $f = 0; print ": "; <>; } 0 } @a;  # 280MB  <--
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* - The amount of memory taken is proportional to the number of elements. It doesn't matter how much memory each of those element takes.

Also, will the use of direct access the array index make the grep slower?

I don't completely understand what you said, but the answer is clear: Write a Benchmark test to find out.

Updated: Added code snippets.