First consider that most of the things you own were probably made in China.
Second note that there are many jobs that are internationally outsourced.
Now if you ever used antivirus programs, instant messaging, cell phones, or Motorola products then you have used a product of Israel. Is that worth nothing to you? Beyond that, consider that Israel has the third highest number of companies on the US stock market (the first of course is the USA and the 2nd is China; being 3rd is usually not impressive but considering that Israel is very small and has only about 7 million people it is noteworthy at the very least). Now why does this matter? International relations. No nation can survive alone and Israel has contributed SO MUCH to the USA; the USA equally contributes back.
Now what you possibly do not know is that Israel is a western democracy with a constitution VERY similar to the US constitution. I am not saying you possibly don't know this due to ignorance but rather given the media image of Israel. Remember: most US news networks do not exactly show the basic everyday life of someone in America. But you live in the USA so you know what it is like. Similarly, the media only shows the newsworthy stuff. Most of it revolves around the Arab-Israeli conflict. Many Muslims (not all, of course), especially in some middle eastern nations, have many problems with the democratic governments present in the USA and in Israel. Often, such extremist Muslims perform acts of Jihad, which are mostly terrorist attacks. The organizations that planned 9/11 - very similar organizations are ones that attack Israel on a fairly regular basis.
So why is all of this important?
Well, here is a fairly simple list
1) Having movements be pro-Israel is NOT the same as putting another nation ahead of the USA; it is merely expressing concern to an ally. The best example is to consider our relations with China: we want to be on good terms with them since they provide us with a lot of goods and we owe them a very significant portion of the current deficit.
2) Lobbying for pro-Israel ideas is lobbying for democracy. As I explained earlier, Israel is VERY democratic (and yes, there are Arab officials in the Israeli government including a supreme court judge, for example).
3) To address your treason argument; you are partially right. Yes, comradery with another nation CAN be considered treason but there are conditions to it, including if the other nation is in bad relations with the nation where the supposed traitor lives. Remember: Israel is on pretty good terms with the USA. Supporting Israel is not an act against the US government. Now I do not know where your ancestry lies but unless you are purely Native American then you have some old world ancestry. Do you feel no loyalty or connection to that nation? (note I am not asking you to choose that nation OR the USA). One can have multiple loyalties especially if the two loyalties are allies.
To summarize and answer your questions simply:
There can be Jewish Americans who lobby US Government for pro-Israel issues because they care about Israel.
Yes, they are real Americans. Remember - Israel and the USA hold very similar democratic values and supporting one is supporting both.
Those lobbying for pro-Israel ideas are not necessarily putting Israel first; they are concerned about the (ancient and current) home of many of their people and most likely believe that stronger relations with Israel will be beneficial for the USA.
To respond to your additional details: Not necessarily. The best example is myself. I am a Jewish American but I was ENTIRELY against Israel's plan to preemptively attack Iran. I admit there do exist conflicts of interests but the loyalty depends on the individual and one must still consider more than the small scope of the single situation.