First, you have to be familiar with fighting. If you're not, you need to research whatever sort of combat your people will be doing!
Keep your sentences short and exciting -- short sentences move the action along quickly.
Use all of the senses -- describe what the character sees, smells, hears, feels, and tastes. Especially include emotions.
fight
a fight
conflict
a fight
Duel
Rapport is the medical term used to describe a relationship of understanding between two people.
That form of combat is called "Jousting"
combat is another term for skirmish's between two or more hostile forces.
Combat between two airplanes.
two people or more in a fight ie. combat
A bond between two people can be described as a strong connection, a deep attachment, or a close relationship. It can also be characterized as a shared understanding or an unbreakable tie.
This would be a fight, a duel, a battle, a joust, a tilt, a contest, or a match. Use a search engine and type in "synonym for combat" to get a longer list of words.