Can you tell me if these are correct?
At Level 1, the Occultist picks two Implements, each one has a Resonance Power, a Base Focus Power, and you pick one Focus Power from the list.
At level 1, you pick one knack and one (level 1) spell from each of the two chosen Implement schools. So that would be two knacks and two level 1 spells. If your intelligence modifier is high enough (from the core rule book) you get one extra spell at level 1 and pick it from either of the two chosen Implement schools.
yes
yes, no.
So yes, you have the focus power and resonance power down.
Also you're right that you have 1 knack and spell known for each implement school.
here's where you went wrong.
If your intelligence modifier is high enough you get extra SPELL SLOTS aka SPELLS PER DAY. This number is the number in the table, at lv1 you get 1 lv1 spell cast per day. If int is high enough you get +1 to that for 2 spells you can cast per day.
So normally you know 2 spells and can pick one of them to cast each day. High enough int and you know 2 and can cast 2. So you can cast each once or one twice.
Your spells known are never modified by stats, this is true for ALL spontaneous casters.
Not quite.
If your intelligence is high enough you get one extra spell* you can cast per day. See the second paragraph of the spells section.
So your second para becomes something like:
At level 1 you know 2 knacks and you know 2 1st level spells. You can cast one of your known 1st level spell/day and you can cast another 1st level spell/day if your intelligence is high enough*.
*for completeness - if your intelligence is 20 or higher you can actually gain 2 or more bonus first level spells.
You get two Implement Schools. For each one you have a Resonant Power, a Base Focus Power, one Knack known, and one first level Spell known.
Additionally you can pick one Focus Power which can be from either of the two schools.
High Int only gets you additional castings per day, not additional spells known.
Edit: Double Ninja'd due to weird connection issues.
Thanks for getting me straightened out.