Question about Camping

Most campgrounds are at the basic end, it's relatively few that have internal kitchens, etc. If this is important to you, I suggest individually researching the campgrounds you intend to stay at. The bigger ones tend to have websites describing their services, etc. Here for example is the list of services at the main Laugardalur campsite in Reykjavik http://www.reykjavikcampsite.is/displayer.asp?cat_id=20

electrical sockets to recharge my batteries etc. Will these be available to use at campgrounds?

There would often be electric sockets available where there is a kitchen, etc. I have seen people recharging things at them on an informal basis. I've not seen a secure system for doing so, it would be up to you whether to risk it. Maybe with the increasing use of expensive mobile devices people might decide there was money to be made from offering the services of securely recharging your device for a fee, but whether that is happening I can't say.

At some camps there is special places for that (at warden office for instance). In other camps people are charging their phone at any sockets they can find :-)
You can get electricity at your tent actually - many camps have electrical "point of access" but you need a special cable (used by motorhomes). Such short cable (0.5 m) can be bought at gas stations here.
In many places like cafes/gas stations you can get access to electrical socket as well.
As a tip - many campsites have a swimming pool nearby. So while taking some pleasure at the pool (and shower) you can ask folk at the desk to charge you phone (just do it in polite manner).