Thats a pretty hard core ride.
You can use pedals.
Yes. All batteries last longer if you are easier on them, both discharge and charge. Buts a charger is not tough on a battery unless its a big charger. Regen can be like 20 amps max this is agressive but not long charging like a charger. Up hill discharge down hill regen it all makes heat in the battery and taking away from the electrodes..
Small batteries cost less but if you push them, they last less long. It is almost a price comparison.
I once made a solar panel on my trailer which was 1.2 amps all the time in the sun. I use a trailer a lot and I live on flat terrain mostly so this didnt make much difference to my stress on the battery. I found the solar panels made better watts on the roof then charged into another battery for recharigng when I" got home rather than on a trailer maybe in shade, maybe not faced to the sun, maybe being stolen. :-|
All you can do is live with your purchase and see how it goes and tell us and we all learn from your experiences.. If this pack doesnt make you happy in life span for your uses, get a bigger pack..
You can tell how much your battery is flat by how much it charges. If you have a 10 ah pack and a 2 amp charger it will take more than 5 hours 2*5 = 10 ah to charge from flat. Charging is not efficient 100% so maybe 5 1/2 - 6 hours and maybe a few to balance.
Also remember when you come home it is a lot of down hill, is it not?. Please take this into account this when considering the life span off your pack. This is not so bad when you think of it.
As much as you ride up hill you will always ride the exact amount down hill. This can not be cheated unless you walk or transport the bike by any other means than riding.