Is there a standard height of navbar and a standard font size for mobile devices?
No not really. The navbar height will be down to the designer and the design of the nav.
There are of course recommended target areas for elements that need to be touched (such as the hamburger menu) which may in itself lead to many navbars being of similar height.
Generally you would want the readable copy text on mobile to be at least its default of 100%/ 1 rem (generally 16px). Anything smaller than 16px on mobile is quite hard to read so I would avoid going smaller for any paragraphs of text.
You may get away with equivalent to 14px for non important text or single word menu items but once again if the text is a link then the target area needs to be big enough to click.
Not Standard size but navbar maximum height 80px and minimum 45px it will be looking good. Font size 15px to 16px its looking good.
Have you tried Google’s Mobile friendly Tests