Confused about great circle navigation

Not that it matters terribly much, but there's a few things I don't get.

On a WAC, which is a Lambert chart, a straight line is more or less a great
circle, right? However, to fly a great circle, you have to constantly adjust
your heading. I still can't conceptually work out why, I must say. Any
pointers?

If you had a WAC chart that displayed the entire Northern Hemisphere on one
chart, you could draw a straight line from Los Angeles to New York. Wouldn't
this be a great circle? And if it is, why couldn't you just fly the single
heading of that line? Is it that because of the fact that a chart that big
would have different magnetic north references at different meridians, and
what you would actually be drawing is a rhumb line?

And speaking of rhumb lines, if you fly one by keeping a constant magnetic
heading between two points, does that mean you actually describe a curve
over the earth's surface?

Thanks in advance, because I'm pretty confused.