Tesla also plans to have cars in multiple price ranges; it sounds like they plan to have three within the next few years (the Model S, the Model E, and the Model X, and yes I realize the pun they built into the model names, they also trademarked "Model Y"). One of them, the Model E, is going to target that $30k price point (at least after rebates), although the reports are that the range will be in the 200-250 mile range rather than the 300-350 that their current top-end cars get.
In terms of increasing the range, that should improve gradually over time as the cost of battery cells go down. That was the point of the $5 billion dollar GigaFactory that they're building, to reduce the cost of lithium ion cells. The primary goal of that is to reduce the cost enough to hit the Model E's price target, but it also has the benefit of enabling higher ranges in the luxury cars where they can spend more money on the battery, albeit at the expense of weight. I know that they're working on longer-term solutions to improve range. They got some patents recently that relate to combining metal air batteries with lithium ion batteries in a hybrid power solution designed to circumvent some of the limitations of metal air batteries (they have the potential for higher densities, but have poor cycle life), although that stuff is a rather long way off.
In terms of ubiquitous fueling stops, they're working in that direction. They're hitting a steady pace building new stations, and by the end of 2015 should have most use cases covered between home-charging overnight and superchargers for distance drives. Automated battery swaps may help too.
Their success isn't a sure thing, but they're definitely making progress towards solving the problems.