Hello, I'll take a stab at your question. The terms you listed actually have a lot of variation, some are officer ranks while others are very different. I'll just go through and answer to the best of my ability.

Hussar - A type of cavalryman who fights with a saber. Light cavalry, generally considered dashing and prestigious.

Cornet - A type of musical instrument. Not sure on the context, but it may perhaps be used in short-hand to refer to the person that plays the Cornet. It's basically a type of trumpet.

Colonel - middle-high ranking military officer, just below 'General'. Generally an important fellow in the era of Tolstoy, who would command a 'regiment' of around a thousand men.

Staff Officer - a officer in the service of a General or some kind of high command apparatus. Generally more concerned with administrative, or military planning functions than with leading men into battle. In most armies, being a Staff officer was considered a safe posting with high chance of promotion.

Junker - was a type of German aristocrat or landed nobleman. It may have been applied to German community leaders in the Baltic States (which Russia controlled at this period). It's doubtful this would be used as a short-hand term for a Russian aristocrat but without knowledge of the context I can't be more detailed.

Regimental/Battalion/Companies are just the building blocks of military units. A regiment is made up of battalions, which are made up of companies. Recall that a Regiment is made up of 1,000 men, give or take.

Commander in Chief - Generally refers to some kind of overall commander of the military. Hence, for example, the US President is often called the 'Commander in Chief'...in theory, the highest level of military authority.

Cossack - Cossacks were an ethnic group of war-like people who lived mostly in modern day Ukraine, and although a source of frequent rebellions were also prized as cavalrymen and soldiers by the Russians. Pretty interesting people with a complex history, worth a topic of their own.

Captain - Mid level rank above Lieutenant, but several grades beneath Colonel. Generally comands a Company.

"The Guards" - Refers to a special class of soldier that was a part of one of the elite 'Guards' regiments of the Imperial Army. The Guards weren't exactly a small unit of bodyguards, they were a military force of thousands of men divided into different regiments, although they were often in charge of the Tsar's security and upkeep of the regime. Being posted to The Guards would be a prestigious post.

Prince - generally a title denoting that someone is a member of the royal family. Hence it's not explicitly a political or military rank, but Princes often held a lot of political and military positions.