Free cancelling is done for many reasons. In juggles it's to prevent dropping them. For example if you do KK7K 6P+K and decide to pause instead of free cancel before pressing P you might get 6P+K P, which is Kasumi's hoshinpo elbow, instead of a jab.
It is also done to stop Kasumi's strings at safe points. Since her strings are highly unsafe you should rarely finish strings with her and be free canceling 95% of the time. Also keep in mind that just because you are safe doesn't mean it is ok to keep attacking. Alot of beginners make that mistake and get blown up for it. You have to use your judgement.
As for your Kasumi I would advise you to go over her frame data. You attack out of blatant disadvantage often and it's getting you counter hit because you should not be doing that. Also you play unsafe with her. I saw 4PP coming out without it being hitconfirmed. Stick to 4P for counter-poking and use 4PP only in stun or on hit confirm. I also saw 66KK a couple of times and it's a good thing that you hit the opponent with it but you have to be careful when you use moves like that. If that had been blocked you give your opponent a free super launcher throw. Stick to 66K and vanilla 66KK if you are trying to get in on somebody. Use 5U 66KK only when the opponent is stunned or if you are whiff punishing something and you know that 66K is going to hit.
66P is a nice move to use to close distance though it's main function is a whiff punisher. Make sure that when you are using it you use it at a range where it will make contact with the opponent. It's risky using it anytime else because the follow up is a high so if you commit to 66PP you'll get crushed for whiffing it or whiff punished.
When you have Kasumi at distance you want to learn how to move in without relying on 66P, 66K and Hoshinpo strike followups because although those moves are decent you are at disadvantage on block, whereas if you space properly and have good footsies you can get within range for her 3K, 4H+K, H+K, P strings, 6P / 3P strings, or even 2P which all leave you in a better position than 66P and 66K on block IMO.
That's all I have for you. I am by no means a high level Kasumi player. You should talk to Allan Paris; He has the most Kasumi knowledge out of any player and will be sure to set you on the right track.