

I'm new to D&D and I've created a wizard character but I'm so confused by how many spells they get. I'm using this character builder to guide me through the process but if I'm reading the rules right I should have additional spells. (https://www.aidedd.org/dnd-creator/index.php)
My character is a level 7 Illusionist wizard with 20 INT. This is what my spellbook looks like (see images). I'm not sure if I receive additional spells from my intelligence bonus or just more spell spots? I'm confused about that too.
If I understand the rules, my spell book starts with 6 spells and I gain 2 more spells every time I level up. So at LVL 7, I should have 12 additional spells, right? 2 spells per levels 2-7.
Then, because I'm an illusionist, there's this bit of text: "Gain an illusion spell from the Wizard’s spell list for every level of wizard spell slots you have and gain another illusion spell each time you gain a new level of wizard spells. These spells go into your spellbook.
If i read that correctly, that means I receive a free illusion spell at LVL 2, 3, 4, 5, 6, 7 and bonus illusion spell ar LVL 3, 5, 7 for opening up the next level of spells I can cast.
If I add it all up, I should have an additional 21 spells as a LVL 7 illusionist wizard. Does that sound right or am I missing something?
Any feedback or advice is appreciated!