The internet on my lumia 710 is working irrespective of entering an APN or not. So, my question is whether setting an APN has any advantages or speed boost. I mean rather than mobile inquiring the operator for APN, I am telling it myself. So does it make any difference or I should leave the APN blank
Normally APN settings should be deployed automatically or rather are not required in the most cases while roaming in your home network because they are set/corrected by the provider on the network side.
But as this is only being done by your provider in the home network you are required to have the correct APN set during roaming in a foreign country's network.
So my advice for you is to check and write out/set the correct APN settings for your provider before you try to use data roaming abroad.
About the question of a performance boost by setting an APN, I can say "no" since the provider just corrects the setting to fit the default APN - so there's no difference in performance to be awaited.
Edit: In the German O2 support forum I read an information from an O2 employee saying the following (I translated the essential information for you):
If a wrong or none APN is set this erroneous configuration is corrected by the provider on the network side to match the default one. When you're abroad this does not work and you have to set them manually.
Here is the link (in German): http://hilfe.o2online.de/t5/iPhone/Warum-wird-der-APN-quot-internet-quot-in-den-offiziellen/m-p/58318#M4344
(This topic covered a difference between the two available APNs available in the O2 network and the difference between those two but I don't think this would change the answer.)
I really don't know much about actual APN settings, but if it works, it works. I won't worry about it. When in doubt, you can always ask your mobile operator for more information.