How can I create an CABasicAnimation for multiple properties?

You can create an CAAnimationGroup and customize the duration and timing function on it. Then you create all your CABasicAnimations, set their to value and add them to the animation group. Finally, you add the animation group to the layer that you are animating.

Here an example:

CABasicAnimation *makeBiggerAnim=[CABasicAnimation animationWithKeyPath:@"cornerRadius"];
makeBiggerAnim.fromValue=[NSNumber numberWithDouble:20.0];
makeBiggerAnim.toValue=[NSNumber numberWithDouble:40.0];

CABasicAnimation *fadeAnim=[CABasicAnimation animationWithKeyPath:@"opacity"];
fadeAnim.fromValue=[NSNumber numberWithDouble:1.0];
fadeAnim.toValue=[NSNumber numberWithDouble:0.0];

CABasicAnimation *rotateAnim=[CABasicAnimation animationWithKeyPath:@"transform.rotation.y"];
rotateAnim.fromValue=[NSNumber numberWithDouble:0.0];
rotateAnim.toValue=[NSNumber numberWithDouble:M_PI_4];

// Customizing the group with duration etc, will apply to all the
// animations in the group
CAAnimationGroup *group = [CAAnimationGroup animation];
group.duration = 0.2;
group.repeatCount = 3;
group.autoreverses = YES;
group.timingFunction = [CAMediaTimingFunction functionWithName:kCAMediaTimingFunctionEaseInEaseOut];
group.animations = @[makeBiggerAnim, fadeAnim, rotateAnim];

[myLayer addAnimation:group forKey:@"allMyAnimations"];