Can you kick your horse and/or use your whip in dressage?
No. Because that is not what dressage is about. Riders engaging in such conduct will inevitably be eliminated. Also, whips are prohibited at the FEI or international levels of the sport. Try watching videos of events like the Olympics or the World Equestrian Games sometime. You'll quickly realize that none of the riders competing in these events are carrying whips of any kind, not in dressage. Eventing and show jumping are different and have different rules, but even there, there are limits to what kind of whips can be carried and how they can be used. There are penalties for excessive spur usage, too.
No. Dressage is not about whips and kicks. You, learn more.
Judy and the Beast
Sure you can. Just don't expect to place higher than a rider who does not need to do that the get their horse to respond well. Dressage is about relaxation and harmony, not kicking and whipping. And, horses sometimes need a good whack if they are being disobedient. But, you aren't going to be getting a ribbon for it.... Life is all about understanding consequences.
Not in competition. The goal is to make it look like you aren't giving the horse any commands. If you have to kick, you've haven't trained the horse sufficiently or you haven't been trained sufficiently.
Dressage means "training" and derives directly from the military use of the horse. If you'll watch videos of Cadre Noir or the Spanische Hofreitschule Wien, the use of any aids at all is nearly undetectable. (You don't want the enemy to be able to see what you are about to do.) You should aim for that level of expertise, but of course you cannot expect to attain it immediately. I've heard that cadets at the Spanish Riding School spend two years riding on the longe without reins or irons, attaining full control with seat and legs alone.
Rules vary by level, and by eventing dressage vs. dressage.
Sure. Just make sure That his cores are full.
If you need to kick your horse or use a whip to get it to do anything you need to improve your riding skill or look at why your horse is being that sluggish in the first place. EDIT: HAHA pissed off some snowflakes