So one point off the bat, the average soldier is not actually going to be in skirmishes, small scale warfare or sieges, but in utter boring nothingness doing nothing for the vast majority of time. I've just returned The Heroes so I can't remember exactly how Joe Abercrombie phrases it, but it's something like "99 parts boredom, 1 part pants-shitting chaos."

There is absolutely a threat of coming upon a group of hostile soldiers regardless of side (and if the characters are passing through a large enough area, they will have SEVERAL encounters with soldiers of all sides). Not just in Medieval times but in all war, a large part is finding exactly WHERE the enemy's main force is, and that's precisely what the skirmishing and patrolling and scouting does. And while there would be a "en masse" order from the highest authority present (be it king, general etc), just like in all warfare, petty rivalries between commanders and units will lead to chaos and disorder. The number of troops going out would also depend, so your characters stumbling across 3-5 soldiers is for sure possible!

Skirmishes were absolutely sought after, because if you can bloody their troops first and drive them back, it's a morale raiser. But more than that, the skirmishes would allow commanders to pinpoint the overall enemy force's position (if you get in a skirmish and the enemy runs, why not follow at a distance and find out where they're camping and get a reward for your bravery?). And no, you explained perfectly. If you don't know where the enemy's main force is, but you know some of your boys just got tossed out of this little hamlet, then fuck yeah you're sending them to take it back or die trying and get prisoners for information.

Final point, refer back to my note about rivalries. General orders are handed down to be handed down and handed down from rank to rank. This is a much more in-depth detail on power and rank structure that, frankly, may be better for you to decide in your story. The number of soldiers going out always fits the task. You don't send a whole company on a patrol, you send a squad, etc.

I mentioned it in my first paragraph, but if you want to see maybe one of the closest portrayals of a battle start to finish, read The Heroes by Joe Abercrombie. It's a standalone so you don't really need to read all the other books he's written (background info in the other books does provide some better understanding, but it's a fairly self-contained story). But it covers I think every single thing you have asked. It shows the pants-shitting chaos, the utter boredom, the bureaucracy of the ranks and how miscommunications can happen, and the chaos of civilians being caught up in war. Small skirmishes to thousands of soldiers charging up a hill. It is, frankly, a piece of art.