You have a couple of things going on here, but neither one if them is likely very serious. Was the oil on the top part of the spark plugs or down on the inside? Oil on the middle to upper part (where the wrench fits on) means a leaking valve cover gasket. Very common and not difficult to replace. You can do it.
In theory, oil is a non-conductor. In practice, old dirty oil will short out your plugs and keep the car from starting if it gets deep enough in the plug recesses. You may want to buy new rubber boots to fit on the coils rather than trying to clean the oil off the old ones.
The battery is another matter. Lots of short trips, lots of attempts to start the engine, an old worn-out battery, or problems with the charging system. The original battery in this car will last 4-6 years, depending on the climate. Replacement battery will last a bit longer if you get a good battery with plenty of capacity.