Hello.
No, there are no limitations connected with local emulator. You use your own SQL Server, your own hard drive, in your own house - so it's no fair to limit something.
But i had such a problem that occured because of such a dumb reason - simply my hard drive was full and there was no MBs to store my data. So please check this. It's first reason that comes to my mind about your problem.
3. I am using Azure storage explorer by the Neudesic, does this causing any issue?
No, i don't think so.
4. Do we have to remove any temp data created by the Emulators Storage and Compute, if yes, please let me know how to clear the temp data for more room to the logs.
5. Where do the temp data gets created when we run the application using Emulators in the Development machines?
Yes, you can. You can find a local store for your roles via Compute Emulator for roles - you should click on instance of your role and click Local Store. Then local store for your roles should appears.
If you want to delete all of your data from storage account, click on the Storage Emulator Icon, then Show Storage Emulator, then select all of services (Blobs, Tables and Queues) and click Reset.