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Well, I will try to address each question.
1. a barlow lens will increase your focal length of your scope by the factor shown. So in your case it will increase your focal length by three times. I think this will in your case be 900mm x 3 =2700mm. Now this would be ok if you were to use say the 40mm but not the 12.5 or 4 mm. Your scope does not have the capacity to sustain such high magnification. This is because 2700 / 40 = 67.5x whereas 2700/4 = 675 x. The image will break down and be useless to you. So use your barlow with this scope and EP's of say 25-40mm range. So in answer to you next question the answer is no the image will not be multiplied by 3x. Just the focal length. A good rule of thumb for any scope and its resolving power is to say 40-50x for each inch of objective. In your case you have a 60mm objective which is my memory serves is 2.5 inches. This would mean magnifications of 100-150x are realistic for your scope. The advertised 675 times is possible but will not give a very good image and quite frankly is a lie.
2. The green moon filter can be screwed into the bottom of your EP's and used to view the moon. As the moon nears its full apparition each month it becomes brighter and brighter. When viewing the moon use the filter to reduce the amount of glare and ease the strain on your eyes. Without it you will find that when you look away from the EP you will not be able to see in the dark at all. A moon filter will help reduce this and make it easier to see away from the EP.
3. As to using this scope for viewing Saturn and Jupiters cloud belts. This scope will be very limited as to what you will see. However, I would think that you will see a very small set of rings on Saturn and I do mean small. Jupiter will show two belts and will be a similar size. Unfortunately this scope is only really a spotting scope. However, it is a start to your determination as to whether you want to get really involved in this hobby.
Hope I have helped.
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