The spellcasting ones are way, way too powerful.
Arcane Affinity - Five extra spells, at any spell level, in spells known? The equivalent existing feat is Magic Adept, where when you take your own class, you get two cantrips and one first-level spell. This is D&D 3.0 level overkill.
Battlemage - Look at Elemental Adept. Treat any 1 as a 2, for one type of damage. On a Fireball, that adds 2, maybe 3 extra damage. This spell would turn any 1 into extra 3.5, so that's more than double the benefit, and it's on all damage spells. You want to stack a DC increase - which is literally nowhere else - and ALSO steal something from War Caster? This is way, way too much.
You need to put these on a list with existing feats, and think 'oh, man, I'm not sure which one I want' or else they're not balanced. If those were added to a game, no spellcaster in their right mind would pick up anything other than a) Resilient Con and b) these.