Oil production is given in terms of barrels per day, can we assume this is the same every day?

yes.

the daily output rate changes throughout the year, but these changes are usually small since it is not like they turn the tap on or off - drilling new wells takes months and a several train-loads of equipment, stopping or re-starting a well takes a day and a large truck.

Again, yes, but I wouldn't extend this to a whole year as it probably does vary quite a bit over a years time (watch how OPEC tries to limit supply and influence prices). But a couple of months is reasonable.

pretty much, there are fluctuations in production, which leads to price change, but for the most part, your theory is correct