How would i write the script to be inducted into a new faction that i created? and how do i connect the quest to the Faction? And any other help you guys think is necessary, please share....

The script command you'll want to use is:

Player.SetFactionRank FactionID, 0

This will put the Player in your new faction at the lowest rank. I'm not entirely sure where that would fit into a quest script, but I would guess that it would be something along the lines of:

If GetStageDone QuestID StageIndex == 1 && Player.GetInFaction FactionID == 0  Player.SetFactionRank FactionID, 0  ;Use this line to advance the quest to the next stage indexEndif

Again, that's just a guess. I don't have much experience with Quest scripts.

I'd recommend you take a look at how the vanilla game does it with the Blades faction in the MQ. In particular, the dialog topics that give the player the choices about whether to join or not.

Remember that if this a Faction that is "visible to player" then you need an icon to display on the factions tab, more than one if you're going to allow rank changes for the player. Note that ranks the player can't reach (as with Captain in the Blades) don't need an icon.

Factions also get used for disposition changes among members, or for joint ownership of a cell, or bed, so if this faction is for those reasons, mark it "invisible to player", but your use of the word "induction" makes me think that's not the case here.