You can yes…two things to be aware of though which will determine how to proceed with a new font.
1. Will you be using a font that is installed on people’s computers?
2. Will you be using a font that is “not” on people’s computers?
The first is the easiest because all you need to do is create some CSS to override the existing font of the theme.
If it’s the second one, such as using a Google font, then you need a different method, either a direct link to the font or a WordPress font plugin, like Easy Google Fonts.
What elements were you wanting to change the font to? Also, what font did you want to use?
As for changing colours, if the colour changes work in desktop view but not in mobile, that sounds a bit odd. Quick question…are you using jetpack and it’s mobile feature? If so, this could be why. Or, if you are changing colours but they are not taking effect even in desktop view, what were you changing colours for?