1. Yes, outside the areas where EU has sole responsibility.

2. Yes, within the areas where the EU has exclusive responsibility and to some extent when it shares responsibility with member states.

3. Yes. Any country is free to leave the EU at any time. See Britain.

In that case, I suggest taking a closer look at the definition of "sovereignty". When it comes to lawmaking, if you say that your country can basically do "almost everything" without the EU's permission, "BUT with certain exceptions" it simply means that it is not sovereign. This is not a matter of opinion but of facts. It's binary — either it is sovereign, or it is not.

You just made up a definition of sovereignty that no nation state on this planet fits.

EU countries aren't forced to stick to the union. If they dislike EU decisions, they are free to leave and do their own thing at any time. This is very unlike US states that aren't allowed to secede from their union.

Whether one can opt out or not, whether someone likes it or not, and whether this state was reached voluntarily or by force, is irrelevant here - definition of sovereignty is pretty much clear

Ad 3. If you believe in the European idea, it is not about my country being sovereign but the European people. There's tension in this for sure. Do the Catalans feel sovereign? The Scots? The Californians?

You've also just described trade agreements.