League of Legends (LoL) Item: Seraph's Embrace

Is there a particular order that the passives apply in? For example if a champion has 199 AP before the AP boost from the mana then would the AP boost from the higher mana apply? I’m probably not phrasing it very well but

Quite inaccurate, this item no longer exists, or renamed.

I consider this to be the go to item for mana hungry supports such as Sona, and maybe other mana burning AP champions. Considering she scales best with her ability spamming potential with a never ending mana source, the best item to get early on would be Tear of the Goddess. Once you get this item, it will help Sona with her mana issues and you can now spam your abilities considering you get CDR maxed, the 10% of which you can get off with and upgrade to Archangel's Staff and even a bigger power spike and AP potential with Seraph's Embrace.

If you leave Singed's poison trail toggled on, you will get bonus mana every 3 seconds.

You don't have to hit anything with it, just cast a spell (/be spending mana now). If you're playing a champ with any skill shots, you can shoot them while you're in the base, or headed back down the lane, and get some extra mana that way. Just be spending mana as often as possible if you're mostly focused on building it up.

Every game I try to get this item but I always get up to about 170 - 250 charge on the Archangel's Staff when the game ends. Does anyone know how to get it to full charge before the end of a game? Maybe I'm just not doing something right or not buying it early enough but still I would like to know how to get it to full charge before a game ends.

Arch Angel's Staff.
Also to others it was changed to whenever you spend mana so now it does work with Singed.

What is an AAS

what is the bonus mana cap

No, if you are playing Singed you won't need to turn off the poison trail in order to get the bonus, because you are constantly spending mana while poison trail is on.

Then they've since changed the way the item works. Back when I used to get it (pre-Seraph's Embrace, season 2, and when it used to give +25 mana regen), you had to cast a spell, not just be spending mana. That's good to know, though. Makes it even easier to increase the bonus mana with Anivia.

As for why you aren't noticing an increase in max mana, Seraph's Embrace doesn't give you any more mana than a fully stacked AAS. They just change the amount of mana it gives you in the base stats, and remove the bonus mana part of the item.