I have a couple of holiday weeks between the end of April and the first week of May and I'm wondering if Iceland is a good destination for that period. I've read that 2-3 weeks is enough to visit all the country's sights, so my idea is to visit each one, but I don't know if this will be possible or not due the snow level and other climatological issues.
It depends on what you mean by "all sights". Iceland has a lot to offer and you could spend a whole summer there without seeing everything.
2-3 weeks is however ample to do a traditional "around the country" drive, traveling along the ring road (highway 1), hitting many (albeit not all) places of interest. Such a trip can be done in one week, so you'll have ample time for detours during a 2-3 week long trip.
Being late April/early May, any mountain road is likely to still be closed and many of the secondary roads may be in rough shape after the winter. This will limit you to sights that are reasonably close to the main highways.
At that time of year, you will find the weather will still be quite cold, making camping a less than exciting prospect. Also, some hotels/guesthouses are only operated during the summer, so you should plan ahead a bit on where you are going to be staying.