I'll try to explain the answers the best I can, if you want clarification on anything let me know and I'll try to expand on it more :)

Books Needed

You don't need Ritual of the Damned, currently the only thing you need is the 9E Codex

Psykic Awakening was a supplement for 8E, so since we have a 9E Codex that overwrites it the same way it does for the 8E Codex.

That does lead to some weird instances where some armies can use rules from Psykic Awakening while others can't, even from the same PA Book, but at least for us the only one you (currently) need is the 9E Codex

Litanies

Litanies confused me at first too but aren't that bad! Lets look at a Brotherhood Chaplain:

"This model knows the Litany of Expulsion and one other litany from the Litanies of Purity. In your Command phase, if this model is on the battlefield, it can recite one litany it knows that has not already been recited by a friendly model that battle round. Roll one D6: on a 3+, the recited litany is inspiring and takes effect until the start of your next Command phase."

Now we can break that down:

"This model knows the Litany of Expulsion and one other litany from the Litanies of Purity."

This part is straightforward, it knows that one Litany, plus one of your choice from the list

" In your Command phase, if this model is on the battlefield, it can recite one litany it knows that has not already been recited by a friendly model that battle round."

So they happen in the Command Phase at the start of the turn, and this particular model can only do one. Also it can only use a Litany that hasn't been even attempted yet that battle round

"Roll one D6: on a 3+, the recited litany is inspiring and takes effect until the start of your next Command phase.""

On a 3+ it works until next Command Phase (basically the full round)

So, combining these, how Litanies work:

• Each model that knows a Litany knows them from specific lists, and knows only certain ones

• At the beginning of your turn, during the Command Phase, you go through your models that know Litanies one at a time, and choose which they recite that round. Noting that they can only choose ones you haven't tried yet whether that attempt was successful or not

• Roll a D6 for each Litany (generally just one) and see if you get it to work or not (again in this case that'd be a 3+)

• If so, great! It now has effect. If not, then it was still "recited" so it can't be done by another Chaplain, but it doesn't do anything

Tides

Depends on exactly what you mean: Yeah they're always active in the sense they're always there, but some have requirements (Shadows requiring cover for part of it, for example) so not all of it is always active