So my monitor only supports VGA, but my graphics card can support both DVI and HDMI. If ever I want to use the HDMI setting and use a converter (HDMI to VGA), will it work and will I get higher resolutions?
What is your graphics card?
If the dvi output is of the I form with 4 analog output pins, then a passive dvi to vga adapter will work.
Here is what they look like: https://en.wikipedia.org/wiki/Digital_Visual_Interface
Otherwise, you need a more expensive active hdmi to vga adapter.
Regardless, your monitor will only display to it's max resolution that the hardware permits.