With intuition.library you can use IntuiText->ITextFont->ta_YSize to get the height and IntuiTextLength() to get the width of the text.
With graphics.library cou'd get the height from RastPort->TxHeight and the width with TextLength(rp,text,length). Or use TextExtent() to get more detailed information.
The screen font can be read from Screen->Font (struct TextAttr) or Screen->RastPort.Font (struct TextFont).
The system font is available in GfxBase->DefaultFont or in RastPort->Font after a call to InitRastPort().