What's going to happen to all the car batteries when they wear out? Landfills? Will they run down & need charging even if you don't drive?

they contain lead which is resyclable

Do you mean the lead-acid batteries used to start conventional engine cars? Those get recycled; the lead is valuable. Do you mean the li-ion batteries that run Priuses and Teslas? I doubt that the manufacturers are worrying much about that. They want to sell disposable junk and let someone else figure out what to do with it when it is worn out.

Car batteries are never put in landfill.  Car batteries cannot be recycled  for lead anywhere in America.  Car batteries are collected and sent by ship to Taiwan or other locations in Indonesia and the sub-continent.  Then they are melted down for lead while they release deadly fumes into the air.  All of the other batteries you listed are now, by law, made of metals and materials deemed non-toxic.  So just throw them in the regular garbage.

they contain lead which is resyclable 

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Quick charging, anytime charging, anywhere charging and use of electricity from fossil fuel based power plants for charging are also existing issues with electric vehicles. As of 2019, the recycling of Li-Ion batteries in most cases does not extract lithium since lithium-ion battery technology continuously changes and processes to recycle these batteries can thus be outdated in a couple of years. Another reason why it isn't being done on a large scale is because the extraction of lithium from old batteries is five times more expensive than mined lithium. Recycling processes today recover approximately 25% to 96% of the materials of a lithium-ion battery cell, depending on the separation technology. Involved steps are discharging, disassembly from the vehicle, crushing or sorting, recovery of electrolyte followed by hydro or pyro metallurgical process of extraction. Safety of workers in recycling unit, safety of near by surroundings, safety of mine workers, safety of near by surroundings, disposal to poor and developing nations where there is leniency in following laws on safety, human rights, environmental rights- remain issues.

Most of the time, car batteries can be rebuilt. The small batteries for flashlights, etc. can be disposed of in the regular trash.

Lithium is a valuable resource.   When electric vehicles become widespread, more lithium battery recycling will take place, just like lead-acid batteries are recycled now.

Some countries, like Germany, regularly recycle batteries because of this reason, but other countries don't do so.

I buy an electric razor, then I buy a few replacement blades, but after a couple of years, the blades are more expensive than a new razor, so it gets thrown away, battery and all. Same with phones, and all those other rechargeable devices we have. 

All these toxic chemicals leaking into the water table. When electric car's and home solar batteries start being thrown out, we will have the same issue.