The problem again being one of peakedness - if you've got batteries large enough to take the several megawatts being thrown at them during heavy braking, then they're probably too big (ie. heavy) for the job.
It's the power electronics that are the main issue - and the next generation of fast chargers will charge at up to 350 kW, whereas something like a Nissan Leaf has a max output of around 100 kW, so your average EV will soon be set up to charge faster than it can discharge.
Yes (Toyota's Hybrid Synergy Drive is a particuarly clever way to do this)
I'm a little bit surprised train manufacturers have not really tried something this, because it's efficient compared to not hybridising and is very reliable - that's why a lot of Prius are used as taxis.
Gridwatch has live data on the UK power supply. Currently the supply is dominated by CCGT (47%).
It feels like there's a big debate about the electricity system on here, as it relates to rail electrification, every 6 months or so...
NR electricity consumption is apparently 3.2 TWh in a GB electricity system that consumed 319 TWh in 2017 (that's 1%) and forecasts a similar level in 2030 (Source: 2018 National Grid Future Energy Scenarios). The lights are not going to go out because NR did, or did not electrify some bits of railway. To put it another way: This uncertainty is much, much less than other uncertainties around industrial demand, electric cars, electric heating and so on that the electricity industry manages.
Hypothecating any new demand for electricity to the marginal or dirtiest generator on the system is to misunderstand how the electricity system works. It's either a technical question of "system level" efficiency (i.e. how many TWh of electricity were produced from TWh fuel ), which you can do over a year or half-hourly if you like your spreadsheets with >17500 rows. Or you can follow the money, see that NR buys from EDF and must conclude that the overwhelming majority of rail power comes from nukes.
The electricity system is decarbonising rapidly, so if CO2 is your thing, then the rate of decarbonisation is really material. For this thread, then for some notional CP7/CP8 electrification, then 2017's value (266 gCO2/kWh) isn't very helpful. Instead, some sensitivity testing with the 2030 values in each of the National Grid scenarios seems like a better idea..