"Burner" because that's what it is -- it burns Diesel to produce heat. It doesn't happen inside the cabin, of course. Dedicated block heaters are often electric, parking heaters can be both electric or gas based. Think like a heater for a tent, if you are more comfortable with that.
Typical losses for the electric grid are considered less than 10% and give you a lot of flexibility. It's also no worse than the cost of distribution gas. Maintenance is orders of magnitude lower and expected life time of both solar panels and wind turbines is in the range of 20 years. That can be mostly considered a one time investment at this point in time.
There is no need to assume that there is an excess of renewable energies for the electrification of transport to be a net win. Modern coal plants have a total conversion efficiency of more than 50%. ICE are typically at best in the 25% range. Even with transportation and conversion losses EVs are a win and any increase in renewable use is shifting the advantage further towards EVs.
Buffer batteries can serve different purpose and need to be sized accordingly. If they are meant to cover the day hours only to use solar panels for example, they only need to cover storing the cell output for minutes to an hour, depending on the station use. Let's say the cost of the solar panel is 1000USD / kW peak and you want to store up to an hour. At utility scale a battery like that adds 20-30% to the cost, including one renewal over the expected life time of the solar panel. That's quite feasible already. If you want to also store the electricity over night, we are talking more like 10 hours, still scalable. Properly sized, you can use the Levelized Cost of Energy numbers from the literature as a decent approximation and would end up with something like 15ct/kWh with a fully off-grid operation (wind+battery, solar+battery is a bit cheaper).
Building a charging network is not rocket science. Heck, the classic gas station network started out the very same way. It won't happen instantly and it will certainly take more time before electric long distance hauls are popular. In Europe they have currently a market share for new trucks of 14% for light trucks (below 16t) and 3.6% for heavy trucks (16t+) with a rapid growth. Most of those are used for regional distribution so far, because charging infrastructure is still growing. But it is happening because the economic reality makes them more attractive. As usual, it's not a black and white topic. Converting regional distribution alone covers a large chunk of all traffic and provides motivation for extending the charge station network by proving the demand.