It is as you say, rather a broad question, both in terms of what qualifies as a "mercenary company" and in terms of time span. Even a single company could, in the course of its existence, vary widely in make-up and effectiveness. Let me try to answer point by point:

So How did they operate?

Most companies were mixed units containing anything from heavy cavalry and knights to lightly armed skrimishers. The exact make-up varied widely between companies and eras. The high point of mercenary warfare was 14th century Italy were mercenary warfare was the norm. The men were often German, Hungarian, English, Italian or French, what soldiers were available depend on which wars had recently been concluded.

Tactically speaking, they operated much like any other company, fighting in whichever way the men had originally been trained.

Were there always enough wars to keep them in business? What happened if there weren't?

No. There wasn't and this was a HUGE problem for their respective employers. If there was no one to fight, mercenary companies frequently turned to plunder, even of their own former employers. The Catalan Company is an excellent example of this. After having been dismissed from Byzantine service they devestated large areas of the Anatolian and later Balkan countryside. The city of Sienna is another example, they had to spend so much gold buying off mercenary companies that the city was effectively ruined.

Was looting considered a perk of the job?

Yes but this was far from unique to mercenaries.

How organised were they?

This is nearly impossible to answer. Some companies were very well organized at times. The White Company (or English Company) was for the most part a highly effective fighting force of men-at-arms and missile troops. The Catalan company by contrast was at the end of its existence little more than a very large robber band, torn by internal fighting and poor discipline.

Again, it's really hard to answer these general questions. There have been so many mercenary or semi-mercenary units throughout the very long time periods that can loosely be called "middle ages". Some were fine fighting units, some were effectively robbers and looters in uniform. Some preformed very well in battle, others avoided battle at all cost.

If you want some reading material, I recommend:
John Hawkwood: An English Mercenary in Fourteenth-century Italy by William Caferro
Catalan Company (1302-1388 AD) by David Kuijt and Chris Brantley