Exactly, most but not all.
How do I vote out the (unelected) people in the EU who make those laws?
And how do I vote out the EU president if I think he's doing a bad job?
Same way you vote for anyone else. In fact, most people have more chance of changing their MEP than they do with their MP, since it's done by proportional representation. My UK parliament vote means shit (like about 80% of the country) since I don't live in a "key marginal".
Plus, the "EU president" (whichever post you mean by that) is nothing special. It's not like a USA president that has actual executive power.
I should get more educated on all of this. At the moment I'll be voting to stay because that seems cool I guess? I feel like we should stick together. "We" being the human race.
In terms of how it affects our economy I honestly have no idea. Which choice will most likely have the worst outcome?
Leaving will make the economy worse in the short-medium term. I don't think that's debatable. Businesses and markets hate uncertainty so an exit will be bad - even if the new UK government handles it well. I'd say it'll be at least 2008 or "Black Wednesday" levels of bad, which is to say it'll be painful but we won't have a Venezuela-style collapse.
Long-term is harder to predict. The UK will no longer be part of the world's largest trading block, though we might get some benefit from exploiting our commonwealth links.
Personally, I don't think the UK can effectively compete with the EU. We'll probably have to become a
de facto EU member like Norway and Switzerland if we want to continue our trade relationships, but we won't have any say in the EU rules that we'll still have to comply with.
I think that leaving would mean we have less control over our economy since the bigger partner almost always comes out ahead in trade deals. We'll almost certainly be the loser in bilateral deals with EU/USA/China.
In return, we'll have more control over immigration, though I'm not sure if it'll really make much difference. Both Switzerland and Norway have to comply with EU free movement rules as part of their deals with the EU.