"I have a heat map ... I want to make it look as continous plot as possible, ... I want to make it appear without individual grid borders."
Use imagesc(C) instead. You can smooth out the pixels using several different methods. For example, you could interpolate the values or, if you have the image processing toolbox, you can do a 2D gaussian filter as demonstracted below.
"is there any way to remove the numbering from the x and y axis in the heatmap figure?"
Yes, but it's much easier to do if you use imagesc() by setting the xtick and ytick values.
"Also, is it possible to make a binary color seelection like red(high) and yellow(low). "
Yes, you can change the colormap
set(gca, 'Colormap',[1 1 0; 1 0 0])