Ultimately with the new features of Windows Phone 8.1, do you think that Microsoft is slowly but steadily narrowing the gap with Google Android and Apple iOS?
Narrowing the gap in terms of usability and features, most definitely. But Microsoft may be too far behind in terms of market share to ever hope to compete, certainly with Android. Windows Phone 8.1 is a very nice mobile OS, but it's still suffering from a lack of apps.
I think it's difficult to read into the future. Microsoft are certainly improving Windows Phone, and I've read (sorry, can't remember where) that they are attempting to unify their "OS experience" on different platforms, but catching up with iOS and Android? Difficult to tell.
Apple and Google are also working hard on their systems. Google is working hard to address its main weaknesses (diversity of OSs and non-standard implementations, as well as some issues with security), and Apple have a very fine system which could benefit from better integration into the cloud & with devices. I'm sure they're not neglecting that. Then there's Firefox OS, Ubuntu and other systems. As I mentioned in a response to a another question by you, the most important thing for any OS is the eco-system of apps & services. If MS manage to get more important apps, and their strategy of hard marketing in developing markets works out, then they will make great progress. If app development remains stagnant, the OS will die. If someone else pushes ahead of them in developing markets (I'm thinking Firefox OS here), they will struggle. But that's all in the future, and only my hindsight is 20-20...
One O/S across all devices may be the next goal for Google, Apple and M$. I just hope they provide different UI for PCs and for mobile devices. What works well on a phone and a tablet, definitely does not work on a regular desktop.
That's a really great questions Rajaa. I'll do my best to answer it.
The best solution to Microsoft's problem of diminishing marketshare, that I've heard, comes from the legendary Anand Shimpi, of Anandtech.com. His belief is that Microsoft needs to switch its emphasis from the devices and services market toward creating a single unified operating system, which works the same across all devices. Unfortunately, it looks like Microsoft doesn't see the market in the same way, and so they are focusing on separate operating systems, with separate app ecosystems, for their devices and services.
On the other hand, Android has swept up much of the developer market by offering a mostly unified operating system that's available across all devices. Apple has recently made inroads into creating a single unified operating system by introducing 64-bit into their iOS ecosystem. Some analysts see this as an attempt to finally unify their software ecosystems. So while Microsoft focuses on devices and services, Google and Apple have made inroads into creating a single OS across all devices. A single platform is preferable to software designers, as it allows their apps to potentially capture larger revenue from a larger market.
In other words, by deliberately fragmenting their market, Microsoft is really going in the opposite direction, regardless of the new features introduced in 8.1.