First, as others have said, your bicycle maintenance should be an ongoing process, not a "once every how often". You ride, you feel, you listen, you clean, you lube, you adjust, all in a continuous cycle depending on the amount and type of riding you do. I generally put my bike on the stand about every three or four rides, and of course immediately if there's something out of whack. You need a stand.

In a broader sense though, unlike recreational riders, bicycling seems to be an integral part of your daily life (commuting) and as others have pointed out also, you need to "own" your bike by knowing every inch of it and how it works, and being able to perform all routine maintenance and most repairs. You may need a shop to work on the bottom bracket or true your wheels (I do) but for keeping things generally in tune and running smoothly, you need to be able to work on your own bike. It's not rocket science. A well-built and trued wheel should stay that way for a long time, unless you're really banging them up.

I have to wonder - since functionality and reliability are so important, why are you screwing around with things like folding bikes? Those are the things you throw on the back of an RV so you can pedal around the campground, or take out to the cottage for a weekend, certainly not suitable for an urban commuting bike.

Whether your current bike is suitable is a matter of opinion, and your specific route. I ride a Trek 930 lugged steel mountain bike and I'm quite sure it could handle your environment with ease and I might hit the bumps and potholes on purpose, just for fun. But it's built for that - yours is not. If you think your bike has the bones to handle it, you should at least look at the tires. Larger tires may help a lot if they'll fit.

Do some Googling or search within this forum for "urban commuting bicycle".