In the first, to shift frequency to down you must increase the length of the triangle. I have conference paper will present in MMS2016 in UAE in the next November talk about How to shift down center frequency in BSF with triangle patch.
For gain, I advise you to test the two case separately and then test both simultaneously.
Basically, you need two modes: one @ 2.45GHz and another @ 5.5GHz.
As your main objective is to dual band patch antenna, you have to generate TWO modes: one for 2.4GHz and next one for 5.5GHz. Now, Obtaining TWO broadside radiating modes using conventional patch antenna (rectangular, circular, circular ring shaped) is very difficult as they have limited broadside radiating modes. You can choose equilateral patch antenna (TMz10 mode at 2.45GHz) and (TM20 or TM21 mode at 5.5GHz). Please see 1988' paper by K F Lee, IEEE AP. Otherwise, you can use 30-60-90 patch antenna where all 1st nine modes produce peak in the broadside direction. Therefore, any mode can be excited. Third techniques is: slot/aperture coupled patch antenna where patch will resonant at 2.45GHz and slot @ 5.5GHz. At 2.45GHz, slot size may be larger than patch dimensions. therefore, we can not excite slot at 2.45GHz and patch at 55GHz. These three options will give guaranteed results for generating dual band patch antenna. If you are not comfort with these three steps, you can use trial-error method to generate several slots on patch or fractal shaped patch antenna. This is obviously a time consuming process. It is better to choose any one process among three procedure as mentioned above.