There is a very famous example of a near-economic collapse in Italia in the early years of the Imperial period (33 CE). The Roman historian Tacitus tells the tale (Ann. 6.16-17). I'll summarize but I am not an expert on this; maybe somebody else can chime in with more detail if needed.

Julius Caesar (way back in 49 BCE) had passed a law in Rome limiting the amount of land in Italia that could be possessed by lenders (a standard usury law, then). This law had been intended to be ad hoc, probably to prevent the exit of currency and the fall of land values via insistence on a certain percentage of capital being invested in real estate. The law, apparently, had been largely ignored after the civil war concluded. In 33 CE, 70 years later, the Roman courts decided to start enforcing. Many people were summoned. I don't know much about the reasons for the sudden decision to exercise the law, but I surmise it had to do with rising interest rates in the early 1st century CE, coupled with falling land values in Italia.

The Praetor was alarmed by the number of cases coming across his desk, and referred the matter to the Senate and the Emperor (Tiberius); they in turn decided there would be an 18 month grace period for the guilty to get their affairs in order. This had disastrous effects and apparently brought about a "scarcity of coin" due to loans being called in all at once. The Senate then ordered the big lenders in the city to invest two-thirds of their capital in Italian land, which had further disastrous effects. Land values plummeted even faster, and reinvestment stagnated (probably because the shrewd recognized that cheaper options were bound to come afterwards). There was a banking commission (either created for this event or already in existence -- I don't know which), and Tiberius secured from them a loan of 100 million sesterces at 0% interest for the distressed land-owners, for a period of 3 years. This was enough to end the cascade and end the crisis.

Yes. Premodern economies could and did have recessions. The Daoguang Depression is an infamous one at the end of the Qing Empire (lasted about 30 years from 1820 or so to 1850). There are some who argue the recession never existed. Most scholars agree it happened. The reasons why it happened are studied extensively by economic historians.... it was a bad time to be in Chinese.

(Disclaimer: my interest is in China's economy during the Ming and Qing Empires, so my understanding of pre-modern economies is shaped by my study of these two powers; should also note that some discussed elements were more important in China than elsewhere):

First question: what was the makeup

Quite frankly, the vast majority of people before the industrial revolution were farmers and economies were dependent on agriculture. There were people engaged in fields which were "non-agricultural", but all of these fields (I struggle to name ones which were not) were dependent on the prosperity of farmers - who comprised the majority of the population. In China, for instance, 65% of economic output was agricultural production during the Qing Empire (1644 - 1911) - there are many sources for this number. As agricultural output was a function of rainfall (environment in general), seed prices, soil quality, so on so forth, a decline in any of these factors would lead to a decline in agricultural output. A severe enough decline in agricultural output would lead to a dramatic fall in GDP. Did people know there were economic problems? Of course, when farms in an area fail to produce food for whatever reason, prices skyrocket, you can't afford to buy food, and you starve to death. This leads to the second question....

Second question: how did people make money?

Commerce dominated pre-modern economies. Trade of various goods and services (rather than industrial production) through personal networks was vital. In other words, trade, trade, trade. So, congrats, your now a farmer living in some premodern economy and there is a famine. How will you survive? Well, you need to eat, perhaps you have a little money saved up or you can meander on down to your local pawnshop or bank and ask for loan at interest (may not get that loan though, or be able to afford it, because interest rates have just spiked - see "Corn at Interest: The Extent and Cost of Grain Storage in Medieval England" by Donald N. McCloskey and John Nash and associated works such as "CAPITAL MARKETS IN CHINA AND BRITAIN, 18TH AND 19TH CENTURY: EVIDENCE FROM GRAIN PRICES" by Wolfgang Keller, Carol H. Shiue, and Xin Wang; plus you do not have collateral. Interest rates are dependent on the variance in prices throughout a given harvest cycle, since the harvest was bad, base line interest - absent risk adjustment - skyrocket due to a steady demand for agricultural products and falling supply.) Or, you have linkages with some friends in a nearby village who did not have harvest issues, this means you can go there, buy grain on interest (e.g. friend gives grain, you sell grain, you pay back friend), eat some, and sell some to the rest of your market. Since a lot of people may be doing this, supply rises equalizes, prices and interest rates begin to fall, and the crises is averted.

The point here: the effect of an economic shock to a single area depends on the strength of interregional networks (i.e. can the problem be spread around such that there is no longer a problem?)

The second point: many people would make money, by acting as middlemen and taking advantage of arbitrage opportunities (i.e. if prices are low in area A and high in area B, middlemen buy in area A - raising the price - and sell in area B - lowering the price).

Third point: personal connections determined whether or not you live or die during a crisis (in other words, you want friends who are not living in your village.)

Interestingly enough, there is work on how this process evolved in China through the Qing Empire. One explanation is that a decreasing land - population ratio (amount of land per person) led to increased individual specialization (see for instance: "From Divergence to Convergence: Reevaluating the History Behind China’s Economic Boom") which would imply stronger networks. Recent work has implied this process did not occur and interregional networks became weaker ("Assessing Market (Dis)Integration in Early Modern China and Europe"). I wonder whether or not intraregional networks strengthened while interregional networks weakened meaning economic shocks would be isolated one area or another... regardless...moving on.

Third question: how about that money?

So, we have all of these people buying and selling stuff. They are not just bartering (maybe at one point they were, but commonly accepted mediums of trade - money - have been around for a while.) Shocks to the quality or quantity of money available have an affect on price and output. Depending on the timing and severity of monetary shocks, this can have a bad or good effect on an economy.

Quality fall (almost always bad): if the quality of money falls - or is perceived to have fallen - for whatever reason, business people take notice (this occurred quite frequently in Spain, under the Habsburgs and in China, under the Yuan, Ming, and Qing) and individual businessmen increase their prices - a given unit of currency buys less goods. Such a price adjustment may not accompany a wage adjustment, so less goods are bought and sold which, in a nutshell, depresses economic activity.

Fall (rise) in money supply: if the money supply falls (rises), the amount of currency per good falls (rises) and business men wanting to attract more currency lower (raise) their prices. Overall, the effect of economic activity depends on the severity of change (some inflation can be good, to much inflation has an adverse effect on economic activity; deflation though is almost always bad because it means there is less currency flowing through the economy.)

Fourth question: are there international effects?

Yes. I am most interested in China, so my knowledge in this area is lacking. However, this is something others may be able to answer. I know that China's appetite for silver dramatically affected the stock of silver within Europe as a whole (1/3 to 1/2 of all American silver ended up China, estimates vary... it is difficult to track global silver flows in the 1400s to 1900s and they were quite unreliable.) There is likely some connection between Chinese economic activity and inflationary pressures in Europe. If you want to learn more about global silver flows, Dennis O. Flynn is an expert in this area.