You are getting somewhere; however, you need a good software package and "Ancestral Quest" is one of the easiest to use and not very expensive.
You must follow certain rules from the start.
1. Always write to correct Greek name. If sometime in the future you seek information in Greece, they must understand you. No point asking about Steve when you mean "Isidoros" or "Stellios" or "Stephanos", etc.
You grandmother is "Chryssa". Chryssa from "Chryssanthi", "Chryssa" from "Chryssoula" or "Chryssa" from "Chryssi" ? He is not "Poulos", her husband was Poulos. What is her maiden name?
2. Greek names and words do not usually start with "Y" simply because "Y" = "U" in Greek. SO. it is not YiaYia, it is GiaGia, it is not Yiorgos, it is Georgios, it is not "Yialitakis" it is "Gialitakis".
3. Be consistent. If the name is not Greek, use the Latin name, if it is Greek, use the closest Latin letters. Use the same spelling all the time.
"Mosco" is Greek-Italian word. Has no meaning in Latin. Nevertheless, any name that starts with "Mosco", theoretical has (Greek)Italian ancestry. Soon or later an ancestor will appear called "Mosco".
Mosco probably derives from the Greek word "Moschos" which roughly translates to "young, well looked after, nice smelling person". Form "Moschos" derives the word "Moschari" = Veal. A few people think that Mosco derives from Moscow and Moscovitis is a person who originates from Moscow. Vitis has also other meanings (Vita = Life)
Which one is the correct name? Sideris, Sideras or Siderias? All three exist, all are correct but all derive from one. Which one was first?
I guess Sideris. A very common name in Asia Minor (Vryoulla, Gioul Baxe, Mellyso, etc. The Siderias from Chios settled around Bethlehem in USA.
Finally, there is a lady called "Petridis" or "Petrakis" or something like that. If I remember well, she is from Chios and has Sideras(is)(ias) connections.