I had registered buzzmarks.in around 5 days ago. I set it up the same day, the site was accessible for a few hours and then later on it gave me the "Server not found error".
Using some tools I found that the DNS has not propagated fully, if so how was I able to access it for some time after I set it up.
Are there any ways using which DNS propagation can be speed-ed up.
There is, unfortunately, no way to speed up DNS propagation. That said, 5 days should be long enough. It sounds like you may have a caching issue or perhaps misconfigured Name Servers. It is also possible that your hosting provider simply has not yet added your domain to their database.
There are a couple of good tools in your Dynadot account that should help you pin-point the issue. I suggest you do an IP lookup to check your settings and also use the Snapshot tool to get an un-cached view of your domain.
Our website snapshot tool allows you to see what your website homepage looks like. The reason you may want to use this tool is to see if you're seeing a different - cached - version of your website.
To see your website's snapshot, please follow these steps: