What colors do you guys prefer to go into your logos? Can you provide a few examples?

I like the strength, adventure, and excitement of Red, and also like the confidence, security, success of blue...

Could you explain cross in your name? Could I use a cross shape as background?

Although I like the idea of the Cross, the religious perspective is NOT the theme. The "Cross" portion of CrossFit (note the F is capitalized) comes from the idea of bringing many competencies/abilities/functional movements together to form a very well rounded level of fitness. See www.crossfit.com for the Headquarters website. They have a link to what is CrossFit.

Thanks

Will we be receiving criticism on our designs in order to do revisions to taylor them?

Yes