why not: we are waiting him?
It's either waiting for him or awaiting him.
Waiting on is also ok. Usually means someone is late and you're getting impatient but otherwise, same meaning.
because 'we are waiting him' is grammar from the 1800s. nowadays, one waits For someone.
The verb in English referring to await the arrival of someone, like in this case - מחכים לו\מחכים למישהו is wait for. (wait as a verb is being used when referring to a delay in movement or action until some event or time)
If you were writing מחכה with nikud would the kapf have a dot?
If by dot you mean dagesh, then yes. מְחַכֶּה