The window1 drawing has an Escher aspect to it, I can't quite tell
what's going on there. Here (US) weather strip refers to a strip of
felt or rubber or narrow sheet metal, that is applied to a window or
door to fill in the gap betweenb, say, the door frame and the door - to
keep wind out basically. I don't see in the pictures what I would
refer to as a weather strip.

In window1.jpg there's an area in the center that seems to lack paint.

Assuming from my own POV (which could be hopelessly wrong) and from pic
2 that you're referring to an exterior strip of wood that has become
weathered and perhaps rotted, the first thing I'd try is to chip out
some and see how bad it is. I've had a bad exterior window sill before
- the part in the corners of the window was rotted - and i chipped out
the bad part with a putty knife and also removed the caulk. Then I
used wood dough (plasticized stuff, comes in a can, looks like earwax,
dries hard as a rock) to fill in the missing bits, then sand the whole
thing, prime, paint, then caulk. Worked like a charm.

If you need to replace I'd buess the wood is pine or some other
ubiquitous substance, that would be the likely replacement, again
proper prime/paint/caulk is key. Exposed wood, even not painted, can
last a long time as long as the water drains off it. Like old
clapboard siding will still be claboard siding after 20 years, it will
dry out but not necessarily rot away. Standing water in little
crevices is a problem, that's what caulk is for.