Interesting, most words seem to have cognitive relations (i.e. all meaning to walk or move /travel).
Unas preguntitas.
1. Cover = to cover a certain distance (not to cover with a blanket eg?).
E.g. we covered a stretch of 3 miles today?
If you use 'caminar' here would people usually assume you covered this distance
walking or can it be used more generally?
It's asumed walking, unless the context allow us other assumption 
2. To act. This strikes me as interesting because it seems rather different from the other meanings? In the translations list it is said to be 'to behave'.
The "behave" here it's a "way to behave"/camino de comportamiento. it's not very used.
ex: Durante todo el proceso, su caminar fue cambiando de protesta a sumisión
"during the trial, his acctitude changed from rebel to submission"
x: "El Ché hizo su caminar político hasta el final"
"Ché (Guevara) walked his own politic way (acted the same) till the end"
So could one say e.g.:
'Ayer el niño (se?) caminó muy mal durante la cena' e.g.?
NO, No way
3. Flow - Is this pertaining to a river or water flowing or more in figurative speech? e.g.
'El río camina del norte del país al sur' ?
"
water flowing: El Nilo camina de Sur a Norte por varios países........."
time flowing: La nuevos tiempos caminaban por el país y la televisión fue sustituyendo a la radio."
Or can you also say this for instance about tears flowing, or a runny nose?
No, not really
4. If you would use 'caminar' in terms of a journey or trip could you use this regardless of the type of vehicle or transportation (bike, train, car etc) or would it be more usual to use other verbs in that case?
You can use "caminar " in a poetry-way (like with Ché Guevara) but usually you use other verbs (viajar, navegar, recorrer, etc.)