Some UTF-8 characters not being recognized by grep or sed

You haven't said which cut you're using, but since you've mentioned the GNU long option --characters I'll assume it's that one. In that case, note this passage from info coreutils 'cut invocation':

‘-c character-list’
‘--characters=character-list’

Select for printing only the characters in positions listed in character-list. The same as -b for now, but internationalization will change that.

(emphasis added)

For the moment, GNU cut always works in terms of single-byte "characters", so the behaviour you see is expected.

Supporting both the -b and -c options is required by POSIX — they weren't added to GNU cut because it had multi-byte support and they worked properly, but to avoid giving errors on POSIX-compliant input. The same -c has been done in some other cut implementations, although not FreeBSD's and OS X's at least.

This is the historic behaviour of -c. -b was newly added to take over the byte role so that -c can work with multi-byte characters. Maybe in a few years it will work as desired consistently, although progress hasn't exactly been quick (it's been over a decade already). GNU cut doesn't even implement the -n option yet, even though it is orthogonal and intended to help the transition. There are potential compatibility problems with old scripts, which may be a concern, although I don't know definitively what the reason is.

grep is only meant to (and was only initially) print(ing) the lines matching a pattern. That's what grep means (based on the g/re/p ed command).

Now, some grep implementations have added a few features that encroaches a bit on the role of other commands. For instance, some have some -r/--include/--exclude to perform part of find's job.

GNU grep added a -o option that makes it perform parts of sed's job as it makes it edit the lines being matched.

pcregrep extended it with -o1, -o2... to print what was matched by capture groups. So with that implementation, even though it was not designed for that, you can actually replace:

sed 's/old/new/'

with:

pcregrep --om-separator=new  -o1 -o2 '(.*?)old(.*)'

That doesn't work properly however if the capture groups match the empty string. On an input like:

XoldY
Xold
oldY

it gives:

XnewY
X
Y

You could work around that using even nastier tricks like:

PCREGREP_COLOR= pcregrep --color=always '.*old.*' |
  pcregrep --om-separator=new -o1 -o2 '^..(.+?)old(.+)..' |
  pcregrep -o1 '.(.*).'

That is, prepend and append \e[m (coloring escape sequence) to all matching lines to be sure there is at least one character on either side of old, and strip them afterwards.