In addition to all of the great answers above, one thing worth saying about low cost carriers in general (and Ryanair specifically) is that minimising turnaround time is absolutely crucial to their business. While we don't know exactly how much Ryanair's fleet of 737 aircraft cost to run per hour, it's a lot (an upper bound would probably be on the order of $11k USD per hour as you can hire one for that much), we do know that it's going to be earning them exactly zero money sat on the ground.
All airlines are subject to, more or less, the same fuel costs, use essentially the same aircraft (which are always chosen based on their economic efficiency for a given route, which is not necessarily the same thing as their temporal efficiency -- in Japan you find all-economy 747s doing short haul, for example) and have essentially the same (legally mandated) service costs. Turnaround time is basically the only thing that is left for them to compete on.
There has been much academic analysis done about minimising turnaround time; e.g. this article details how operations research has been used to look at the problem. Aviation throws up many interesting problems like this -- several of which are NP hard, and Boeing themselves have produced a document detailing how a time saving on the order of minutes can result in the difference between making a lot of money on an airline route and being faced with some very large shortfalls to make up. Heck, a quick google shows up this Masters' thesis looking at Rynair's profitability and turnaround time. If you'll forgive me selectively quoting the relevant bits about just how crucial turnaround time is to Rynair, they're quite telling:
By taking about half the [turnaround] time of the larger airlines like British Airways (BA) or Lufthansa, Ryanair’s planes made an average of nine trips per day as against the average six of larger airlines.
No other low-cost airline managed to replicate Ryanair’s results. According to analysts, its “cost per available seat mile” (the yardstick used by the airline industry to measure costs) was 30% lower than the average for Europe’s major airlines, and its productivity - as measured by the number of passengers per employee - was 40% higher. As a result, Ryanair could break even when its planes were just over half-full.
I would say that the fact that Ryanair does not tell you which gate to go to ahead of time is because they themselves do not necessarily know. When you add in the fact that Ryanair pays tiny landing fees to most airports (negotiated on 15-20 year terms), it's entirely likely that their gate -- which they might want to squeeze in around other, longer operators -- may be necessarily uncertain until it is clear what has happened elsewhere in the airport.
What's far more important to them is, frankly, that the aircraft gets to a gate and leaves with some (not necessarily all!) passengers as soon as possible. I'm afraid that, as far as they're concerned, you and your grandmother's inability to get to the gate on time would just be another willing sacrifice on the altar of capitalism.