When playing the game, the resolution is about 1/2 the screen resolution. There is no resolution option in the video section. Is there a way to correct this?

There's a fan-made high resolution patch, check the sticky thread in this forum.

Thanks. Unfortunately, adding the patches (using the "all-i-one" link) is causing the main menu to be scrunched to the left half of the screen in odd colors and drawing the right side as solid blue, even after reinstalling the whole game without the patches.

The "all-in-one" link is old, from back in 2010. The top post of the sticky thread was updated a few months ago with newer versions of the patches. You should follow the instructions there instead.

As for the issues with the main menu screen, that's a common problem that I think is related to ddraw. Check, for example, this thread:

https://www.gog.com/forum/arcanum_of_steamworks_and_magick_obscura/huge_graphical_issues_rendering_game_completely_unplayable/post1