So I was watching Death Note, and at a certain point Misa loses her Death Note, her memories, and her eyes. What would happen, if she gets her Death Note back for some reason? - would her shinigami eyes come back?
No she doesn't, this is show later in the series which going by how the question is worded, indicates that the evidence to this would be a spoiler.
in Episode 24 when she retrieves the Death Note that Light buried as apart of his grand plan to exonerate Himself, Misa (to save himself from Rem) and to kill L.
After Misa recovers the book her memories return, however she had forgotten L's real name which she saw back when she was at University with Light and L and so makes the eye deal again
"After the Task Force says goodbye to Misa, Light orders Misa to recover the other Death Note he had hidden and buried at a particular site a few months earlier. Misa goes to the site and regains her memories, while also finding a slip to write down the true name of "Hideki Ryuga," only for her to have forgotten (later revealed to have also been planned). Returning from the Shinigami Realm, Ryuk greets Misa, who makes a second deal for the Shinigami Eyes in order to find out L's true identity (and also trading a human apple for a Shinigami one, which Misa finds sandy). Misa and Ryuk then return to the headquarters and reunite with Light out front, where Rem notices via a security camera that Misa has again halved her life, and now has less than a month to live."