Why were military officers so young hundreds of years ago? Were they capable officers?

You might get a more specific answer if you could be more specific about a country or time period; however, I have written about young officers in the British navy a couple of times. If these threads interest you, let me know and please post any follow-up questions here!

To quote from that first answer a bit:

To become an officer in the Napoleonic period, a man would need to have entered the navy at a suitable age (certainly no older than 14) to build up enough sea time and practical experience to pass a lieutenant's examination, which required that the examining board be presented with evidence that he had spent six years at sea (at least two of them in the Navy) and that he "appeared" to be 20 years old, which was the minimum age to become a lieutenant. And yes, the point of boys going to sea that young was eventually to attain commissioned rank.

In the period of the Napoleonic wars, many boys went to sea as young as 11 or 12 to start building up the required sea time, or were at least put on ship's books by captains who were friends or relatives of their families to start building up the required sea time. It wasn't uncommon for boys to be placed on the books even earlier, and this practice (though technically illegal) was viewed with some benevolence, because as navigation (particularly finding longitude) became more complicated, most boys needed a few years of schooling ashore, particularly in mathematics.

Once a midshipman had built up the required sea time, he would have to sit for a lieutenant's examination in front of a panel of captains, where he would be grilled on practical seamanship, navigation, mathematics, geography, history or really anything else the board wanted to throw at him. There wasn't a standard examination, so it was quite possible that sympathetic boards could pass men rather easily (Horatio Nelson's stepson rather famously became a lieutenant at around 16 and a post-captain at 17, due to Nelson's intervention and "interest" in his future, despite being spectacularly unqualified for the job).

Once a man became a lieutenant, he would have to rely on luck and his own "interest" from sponsors for further promotion. The first lieutenant of a ship was often promoted after a successful action (this was seen as a compliment to his captain, oddly enough). A lieutenant's next step would be as a master and commander of a vessel; he would by courtesy be called a captain at that point, but it wasn't until he was promoted to captain of a post-ship that he would be called a post-captain, or just captain, and be assured of (if he lived long enough) dying an admiral. Once a man was a post-captain, his further promotion was entirely based on seniority on the list of captains. (What's a post-ship? In confusing logic, a post-ship is what a post-captain would command. In practical terms, it usually meant at least a frigate, although sometimes smaller ships were considered post-ships out of courtesy to a captain.)

So yes, it was common for boys to be midshipmen in the navy of the time. They could even command prizes and other ships (certainly with the strong help of an experienced warrant officer and other seamen) as part of their training, or command a ship's boat in a landing or cutting-out expedition. Many were killed or wounded in battle.