The office of the presidency has more power than you think it does. The president is expected to set the legislative agenda, meaning that he or she has a lot of influence over what the houses of congress will talk about. ie, the ability to block the agenda of others using veto power until they agree to discuss certain issues. The past several presidents have had control of at least one body of congress, and the majority leader will usually take direction from the president on what should be on the agenda.

For example, Barack Obama has had an impact on #5 and #7 from your list. He's most likely going to make a big push on immigration reform in his next term, though it most likely won't involve H1-B visas (though he has spoken in favor of the issue, at the urging of his many silicon valley supporters).

Your point is correct that the president is not all powerful. But if he or she really wants to push for any of the items you mentioned, they have the power to make it the subject of national discussion. A president who is particularly skilled at dealing with congress (like LBJ) can go a long way toward turning bills into law.