Are you limited to what shield you should carry based on whether you perk heavy or light armor? There are many more heavy armor shields in the game. If you use light armor, should you avoid those heavy armor shields, like the Shield of Ysgramor?

It doesn't matter. Shields only effect your character via the block skill (and its perks), their weight and the AR they provide. Whether you specialize in light or heavy armor, e.g., has no bearing on shield use (or vice versa).

The armour perks arent affected by the shield weight. The shield is extra. The armour perks are only head, hands, body feet.

If you only use a shield you can still cast flesh spells with the mage armor bonus

If you only use a shield you can still cast flesh spells with the mage armor bonus