Serve showed up in the late twelfth century, coming from the Old French servir and classical Latin servire, both of which basically mean to serve. Now, it’s related to servus, slave, but it doesn’t seem to be related to the suffix -serve. Serve has no further origin, although it might be Etruscan, and -serve has a different history (you’ll see in a minute). They still might be related, but unfortunately I don’t know enough ancient Latin to be sure.
Next, we’re looking at deserve, the only -serve word that’s related to serve. It showed up in the early thirteenth century from the Old French deserver and classical Latin deservire, serve well. The de- prefix here means completely because prefixes are stupid sometimes, so “serve completely” makes sense. And apparently the idea of being served well transformed into being entitled to good service, and that’s why we have deserve.
Observe showed up in the late fourteenth century, coming from the Old French observer/osserver, which is just observe. That of course comes from the classical Latin observare, which has meanings that range from observe to guard to heed. It’s a ranged word, is what I’m saying. It’s a mix of the prefix ob-, over, and servare, save, keep, or preserve. So it’s to over save? Anyway! Servare can be traced to the Proto Indo European ser-, to protect. And it doesn’t seem to be related to serve. Man, how weird.
Next, reserve. It showed up in the mid fourteenth century and it has a fairly similar origin as observe. It comes from the Old French reserver, withhold, and before that the classical Latin reservare, reserve or hold back. The re- prefix is the back part, and with the save/keep of servare, it’s literally “keep back”. Well, at least that makes sense.
Next, preserve showed up in the late fourteenth century from the Anglo French preservare, Old French preserver, and Medieval Latin preservare, all of which mean preserve. Before that it’s the Late Latin praeservare, guard beforehand. The prae is just pre-, before, so the word is “to save before”. I guess that works.
Conserve also showed up in the late fourteenth century, coming from the Old French conserver and classical Latin conservare, which means (dramatic pause)…conserve. Yeah, not a lot of stretching with this word. Anyway, the prefix con- (from com-) is just an intensifier here—amusing aside: several common prefixes can also be intensifiers; I wonder how they decided when to use the actual meaning of the prefix and when to use it as word frosting. So with sevare, to keep, this word is to really keep. Not just save it, but conserve it.
TL;DR: Serve and deserve aren’t related to observe, reserve, preserve and conserve because words are freaking stupid.