I am visiting Tokyo for 5 days, Kyoto 3 days and Osaka for 2 days am I able to use a normal Suica card within these cities?
What exact dates?
Before March 23, 2013 - Tokyo yes, Kyoto - only on JR, Osaka, only on JR.
If you wish to use the subways in Osaka or Kyoto (you probably will) then the Suica won't work and you'll need to buy an ICOCA, or individual tickets.
On and after March 23, 2013 - Tokyo yes, Kyoto yes, Osaka yes. The exception may be the Kyoto buses which currently don't accept IC cards, they might after March I guess.
Am I able to purchase this ticket only when we touch down in Haneda airport then use it straight away to travel to Shinjuku where we are staying
You should be able to buy Suica from a ticket machine near the monorail. Alternatively, you could buy a Pasmo although it is not valid in Kyoto/Osaka until after March 23, 2013.
Although it is not clear from your question you can't use Suica to travel on the Shinkansen from Tokyo to Kyoto, you would have to purchase a separate Shinkansen ticket.
Enjoy your trip!