1) Improving the roads could make the cities grow faster, but rather later in the game when there are enough people using their own cars for traveling (not before 1950). Much better is to use your improved roads for your bus lines between the cities. I am now playing on hard difficulty and these lines are making huge profits (0,5 – 1M/year each!). Do not just improve the old and crooked unpaved roads by replacing them with the ‘upgrade the road’ tool, delete them and rebuild them with better ones with less curves and not so steep slopes.
2) Upgrading the city streets is needed later in the game, when your trams get stuck because of the traffic. I am now not sure, if there are also some speed limits for the trams because of old and unupgraded streets…
3) Destroying the road will prevent the factory from sending the goods to the neighbouring town. I have never seen the game to rebuild any roads I destroyed. But, actually, this is counterproductive. If there are two towns in that region (one with your cargo line and one accesible without your help, each with demand for let’s say 40 pieces of goods), the potential of production for the factory is 80. If you destroy the road, you reduce that potential to 40, so the factory won’t ever produce so much and won’t also demand so much resources from the mine/forrest/oil wells. And you also have the resource line, right? So my suggestion is let the road be and just wait until the factory and the mine/forrset/oil wells increase their production enough. So or so you can never deliver more goods to the city than its demanded amount.