You ask many good questions and several folks have given fairly good answers. I've been working on all my cars and yard equipment for 60 years. I have a 20" rotary push mower that's well over 50 years old still going strong. I maintain my equipment and it serves me well. My Sears lawn tractor was purchased in 1982 and mows like new. I bought Oregon "Gator" high lift mulching blades for both mowers which do a great job, much better than original blades. I sharpen then annually with an angle grinder and a cone type balancer carefully adjusted to make sure blades are centered. Take them off and put them back on to get a repeat check as many times as you think necessary. Others have said blade balance is important and they are correct. Be fussy about this.
Battery chargers have come a long way from old fashioned "dumb" chargers. Left hooked up indefinitely they will overcharge a battery and "boil" the electrolyte away. When that happens the battery is toast. It doesn't matter if it's a "trickle charger" which are typically 1 amp or less or a much higher amp charger, never leave connected past full charge if you use a dumb charger. Do yourself and all of your batteries (I assume you have one or more cars/trucks) a favor and get yourself a smart charger. There are several really good brands. I've had a CTEK MXS 5.0 for years and it has brought several car and lawn tractor batteries back from "the dead". It has a desulfate and a recondition mode which can salvage a sulfated battery. It can't save all batteries but it's always worth a try. I have been using the recondition mode of my CTEK on my cars annually and two of those batteries are now ten years old where I live in a harsh winter climate in upstate NY. Most people around here only get 3 to 5 years from a car battery. They don't know enough to use a smart charger. I paid about $85 for mine and it's paid for itself over and over again. Both of those car batteries still take a charge properly and measure about 12.9 volts when fully charged. Good brands besides CTEK are Noco, Battery Tender, DeWalt, Schumacher. I'm sure there are others. You can pay anywhere from $30 to well over $100, that's up to you but I strongly encourage you to get a smart charger. Read and understand the manual to get the most from your charger.
You say you leave your lawn mower battery not on a charger over the winter. That's not a good idea. As one reply said at least charge it up several times during the winter. It doesn't matter if it's in the cold garage on in your basement, just keep it charged. One of the worst things you can do to a battery is let it discharge because that will sulfate the plates which diminish the battery charge and make it more difficult to accept a charge. A much cheaper option would be to use a Harbor Freight battery maintainer, they have them on sale periodically for well under ten bucks. Just connect it and leave it on all winter. A smart charger can do the same thing, it can be left on indefinitely without over charging. Never let your battery voltage drop below about 12.3 volts or it will sulfate.
I agree with one post who advised running your equipment out of gas before seasonal storage. If you don't want to bother with that, at a bare minimum use gas with stabilizer at the recommended dilution. I also use good name brand synthetic oil in all my yard equipment, it lubricates much better than regular oil. It's no more expensive because you don't need to change it as frequently.