Oil level uncertainty

Sounds like the issue is oil is supposed to spray onto some of the moving parts, and it will run way up on the dip stick. Proper procedure is to remove the dip stick, wipe it off, reinsert it, then take the reading. Even when doing that, on some engines, the dip stick rubs against other parts of the engine block and oil can get spread on part of the indicator area. Look on both sides of the dip stick, then take the lower reading if it is different on both sides.

It is a good idea to check the oil level periodically, then you will become familiar with "normal". To start with, ask the mechanic at your next oil change exactly how many quarts was put in. Please be kind and explain you want to learn what "normal" looks like, not that you do not trust him. Chances are, if he has some free time, he will be happy to show you and explain the service he performed.

Also, be aware that for quite some time now, all engines use a little oil between oil changes, so do not get excited if your level drops. Years ago dip sticks were marked with "Add" and "Full", but to address the many complaints of oil usage, today almost all dip sticks are marked "Min" and "Max". When the specified amount of oil is installed during the oil change, the final level will not reach the "Max" mark. It will be somewhere below that. All that is important is it remain above the "Min" mark until the next oil change. Also understand if the level should happen to drop just slightly below the "Min" mark, there's no need to bail out and head for cover! There is some safety margin built in so there is no need to panic.

If the fluid levels are good, the car should be safe to drive. To say that a different way, if there is a serious problem that must be addressed, adding oil or water will not change anything or fix any defect.

A cooling system flush is probably not necessary. The typical maintenance service when there is no other problem is a drain and fill. Acids build up in the coolant over time. The purpose of the drain and fill every two years is that is how long it takes for the additives in the antifreeze to wear out. Those include corrosion inhibitors that neutralize those acids, water pump lubricant, and seal conditioners. A flush is the better alternative when the cooling system was contaminated with automatic transmission fluid or engine oil, but then that service would be part of a much larger repair, and it would have been included in that repair estimate.

The concern right now is where did the coolant go? If there is no obvious external leaks, and especially if this happens again, consider having your mechanic perform a chemical test at the radiator for a leaking cylinder head gasket. If that turns out positive, that gasket will need to be replaced. That is a fairly big job, and it will include servicing the cooling system. Do not add any antifreeze at this time because if this service becomes necessary, it is going to be drained out and discarded, so you would just be wasting your money. Your mechanic will get the coolant to the right proportions when the job is done.