Yes. Absolutely.
But in the darkest hours we were alone. If we had been overrun then all was over.
Yes, although they did manage to hold back the German blitz.
In any case, logistically, the Germans simply didn't have the wherewithal for a cross-channel invasion. And the British had the finest navy in the world (until we caught up and surpassed you in that area).
I don't think the U.S. would have wanted Britain to go down alone. While there was some isolationist sentiment at the time, it seems a lot of people genuinely thought that France and Britain could have handled the Germans without our help. On paper, they had the Germans outnumbered and outgunned. How was anyone to know that France would fold up and surrender so quickly?
That was in June, 1940, when the U.S. Army was no larger than Belgium's. However, just after that, the U.S. passed the Two-Ocean Navy Act. In addition, FDR called for massive production increases in aircraft, tanks, and other equipment around the same time. So, we knew that we were headed to war, but it took time to marshal all the necessary resources and industries to build up our military-industrial complex.
One thing to remember is that, in the aftermath of WW2, the entire attitude in the U.S. changed. I perceive that there's been a great deal of national regret over what many regard as a short-sighted, xenophobic, and isolationist attitude which pervaded in the U.S. after WW1, which opposed the U.S. entry into the League of Nations. Our military was reduced in size and kept at a minimal level, so by 1939-40, we were woefully unprepared to enter a world war. We weren't even all that prepared in December 1941, but we were getting there.
Ever since then, the U.S. has made it a priority to maintain high levels of military spending and to take a much more proactive (and somewhat aggressive) approach to geopolitics. All of it is rooted in the notion that, "if we had been stronger in 1940, we could have stopped Hitler before he even got started."