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Rules for Synchroing:
1. You need a Tuner monster and a non-tuner monster(s)
2. The combined level of the synchro material monsters must equal the exact level of the synchro monster you wish to summon.
3. All synchro material monsters must be face up and on your side of the field.

Other Stuff you need to know:
1. Some synchro monsters require a specific tuner (type, attribute, or name specific)
2. other synchro monsters may require specific non-tuners (type, attribute, or level specific)
3. some synchro mosters may require a specific amount or minimum of non-tuners.
4. currently, all synchro monsters are semi-nomi.

Incorrect. Greatest examples: Starlight Road and Blackwing - Vayu the Emblem of Honor. There are cards that do allow you to Special Summon Synchro monsters without Synchro Summon.

However, following the same principle as it was for Cyber Stein and Fusion monsters, once they're sent to the Graveyard or Removed from Play, they cannot be Special Summoned again by card effects unless returned to the Extra Deck and properly Synchro Summoned.

This is, of course, following that the common term for "semi-nomi" refers to those monsters with specific Special Summon requirements, and cannot be Special Summoned through any other method unless those requirements are met beforehand. Synchro and Fusion monsters, however, have shown to use such effects that allow them to be Special Summoned regardless.

What is this list?

So many spelling errors, and other problems.

Although I suppose six Stardust Dragons could be considered good Yu-Gi-Oh'z.

The terms "nomi" and "semi-nomi" are popular terms that refer to monsters with specific Special Summoning requirements. For the game currently, I'll use the following two examples:

Chaos Sorcerer: Semi-nomi.
Card Lore: This card cannot be Normal Summoned or Set. This card can only be Special Summoned by removing one LIGHT monster and one DARK monster in your Graveyard from play.

When you see this requirement, you have to especially note the "only". By this text, it cannot in any way be Special Summoned to the field through any card effect, before it meets its own Summoning requirement. Once it does meet this requirement, however, if it is later sent to the Graveyard, you may Special Summon it back to the field, through such effects like Call of the Haunted. If returned to your Hand or Deck, the card's Summoning requirement is reset, and you must meet that requirement again (I believe this also applies to the Removed from Play).

Judgment Dragon: Nomi.
Card Lore: This card cannot be Normal Summoned or Set. This card cannot be Special Summoned except when you have 4 different Lightsworn monsters in your Graveyard.

In this text, you have to note the "except". When that word is included in the Summoning requirement, it means the monster is not in any way allowed to be Summoned to the field except through its own Summoning requirement.