Advanced software (in modern automatic transmissions for example) and material advancements have made all the difference in the advancement of combustion engines in the past 15 years and I firmly believe that technology can be pushed even further. I want to see 4 cylinder engines pushing 500hp, sounds like a pipedream now but so did 300hp when I was a kid.
If you want to see what happens when you perfect the marriage between a combustion engine and an electric motor w/ batteries, do some research on the McLaren P1.
I doubt it. We've passed peak oil and have resorted to expensive techniques like fracking to collect the scraps. Meanwhile, even if no advances in solar panels occur in the future, the price of power produced by solar will only go down as more panels are added to the grid.
The biggest hurdle now is getting cars with combustion engines off the road and replacing them with electric. I haven't seen much progress made on that front in the past few years.