At least 5 hour battery life.
most of them have this much life.
No webcam (I don’t need it)
it’s price is miniature, so all will have it.
3)no speakers. (I am perfectly fine with headphones or external speakers)
same as above.
Linux instead of windows. (Lower price, not a gaming pc anyway)
well windows on PC’s from OEM’s coast’s about 50$, you can ditch it after buying.
Smaller or at the size of an A4 standard paper.
if it is for work, i recommend ~12" ones, which is near A4.
Powerful enough to run Reaper audio program with At least 4 VST’s.
most built in audio cars, are enough.
Not glossy (hate fingerprints)
same as 2).
now you have not much choice, actually i’m disappointed that the market has less than 10 models which defines as good models:
hp elitebook series
ibm ThinkPad series