Regarding the HQ logo, please find below a few ideas and guidelines:
It has to be:
3. Easy to remember
It should reflect the soul of the business, so it has to be:
I believe it would be nice to play somehow with the letters HQ; they can be merged/ intertwined.
Also, the logo should be made in a way that we will be able to add elements depending on the occasion. For example, we can add a football ball (on Sports Day) or a Qatari flag (on National Day) etc.
Regarding the color, maybe keep it black in a white background or white in a black background. Elements added depending on occasions, can be colorful.
Please find below a few examples of logos I liked. Maybe use these as inspiration?