How to scale the size of heat map and row names font size?
heatmap.2 is very configurable, and has options to adjust the things you want to fix:

cexRow: changes the size of the row label font. 

keysize: numeric value indicating the size of the key.

The size of the key is also affected by the layout of the plot. heatmap.2 splits your plotting device into 4 panes (see the picture below), and you can control the size of the key partly by controlling the size and layout of these 4 panes. 



The layout and scale of these panes can be controlled using the lmat, lwid and lhei arguments. For example, in your case, because you're not displaying the column dendrogram in your plot, you could set the height of the first row of the layout to be smaller, which would reduce the size of the colour key: lhei=c(2, 10) (this is just an example, you'd need to experiment to find values which worked well for your specific heatmap).