In order to answer your question it must be firstly ascertained what is meant by 'tavern' or 'pub'. Modern ideas of medieval drinking establishments are much more informed by modern ideas and fantasy fiction as well as isn unholy mashing together of period ideas and terminology. We must then look at the social context in order to understand what the atmosphere in these places was like. I will answer the question mainly with relevance to England rather than Europe as a whole as that is my area of understanding and customs likely varied in other areas.

Firstly we must establish what kind of drinking establishments existed in the middle ages. The modern idea of the 'medieval pub' bares little resemblance to the reality. There were in essence three main types of drinking establishments: alehouses, taverns and inns each one filling a different niche. Inns were for travellers and thus you would not really be drinking in them if you were a local, therefore we may discount them from the question. Alehouses are probably the closest thing to the modern conceptions you have of the period. They were places of low status, they usually served ale exculisvely (brewed on site by the wife of the owner) or sometimes drinks like cider as well depending on the region. Alehouses could get rather rowdy and often proved the haunts of prostitutes, cutpurses and other ne'er do wells. Taverns on the other hand were rather up-market establishments, kept by respectful landlords and catering to the well to do. Taverns exclusively served wine and were often furnished with fine white tablecloths. Taverns were also strictly bound by guild regulations, the landlord was obliged to keep his cellar door open and allow any customer down to view the barrels of wine to ensure they were not passing off cheap stuff as a fine vintage. The landlord of a Tavern was also expected to politely show the drinkers the door come curfew time. Punishments for breaking guild regulations or operating outside of a guild were strict and involved putting the guilty party in a pillory and pouring his entire stock over his head.

Now we come to your other queries. It is very difficult to give any satisfactory answers to your first two as these things must have seen considerable variance however I will say that medieval people were certainly no strangers to drunkenness and as such you can expect a similar amount to the modern day. As for knights and other members of the gentry or nobility, you would almost never find them in either Alehouses or Taverns, they had better quality ale and more wide ranging collections of wine in their manors and castles. Even if you did happen to come across someone of high status in a Tavern or Alehouse you would still have to show deference to them befitting their rank in society. Medieval society as a whole was hugely hierarchical and built upon a bedrock of peoples respect for their betters and charity toward those worse off. Deep societal conventions were not simply dropped due to any surrounding. When it comes to roughhousing, drunken brawls seem to have been a fairly regular occurrence in Alehouses as there is rather perstisant mention of such things in the law court records. As for protection as a commoner and not a member of the gentry you would not be able to wear a sword within the city limits however the wearing of daggers was common.