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.