Now as the official Lumia Cyan update has started rolling out, can I remove/uninstall Developer Preview from my phone. And when the official updates are installed does it overwrite the previously installed updates?
You can, but there's no need to.
If you're talking about the WP 8.1 Preview for Developers OS version, even if you can roll back to 8.0, there's no need to. The preview already contains most of the OS-specific features, fixes and other changes that are now being officially rolled out. All the Lumia Cyan update adds is manufacturer-specific (and possibly carrier-specific) firmware and other changes, and you can install it over the preview. But if you really want to, yes, you can uninstall the 8.1 preview.
If you're talking about the Preview for Developers app, then the answer is mostly the same. You can uninstall it if you want, but chances are you're going to need it again if and when the next preview version of Windows Phone becomes available, so you might as well keep it on your phone.
Microsoft have temporarily suspended rollout of Cyan to phones with the Preview for Developers update installed, due to some issues with Bitlocker that affects corporate customers:
We are currently investigating the issue. We have paused delivery of the [Cyan] update to customers using the Preview for Developers, and will resume once a fix is in place.
In other words, right now you would have to uninstall the Preview for Developers update in order to receive Cyan (assuming it's been released in your country and for your phone model). Once a fix is in place, this will no longer be necessary.