Is it normal that I find it difficult to wake my baby to nurse?

Yes. If the weight gain is adequate, you are probably not giving the baby enough time to get good and hungry. If it is inadequate, more evaluation is needed.
No. This can actually be a warning sign for very young infants. Babies should feed roughly every 2-3 hours and for the first few weeks not feed fewer than every 4-5 hours. Sleepiness can be a warning sign for illness, infection, jaundice, etc. Once babies are gaining weight well, they generally can be allowed to sleep a little longer. Excessive sleeping should be evalutated by a physician.