The Floyd Rose bridge should be parallel with the body; if it is not, you will have to make major and unnecessary adjustments to the other parts of the guitar in order to get a good action and correct intonation/'overall set up' (which you will likely find hard with the bridge at that angle.).
The correct method to bring the bridge parallel is to adjust the spring plate which your bridge is attached to/floating on. (Using a spring instead is perfectly acceptable if it produces the required result and brings the bridge parallel with the body; you may find however that the spring provides too much or too little tension and that you still have to make spring plate adjustments).
This is done by adjusting the screws which attach the plate to the guitar. If you would like to increase the tension of the springs(lower the bridge), then you need to tighten the screws(bringing the plate closer to the body of the guitar).
This is needed if you increase the gauge of your strings, thus increasing the tension of the strings on the bridge. If you put smaller gauge strings on the guitar you will likely have to untighten the screws(move the plate further from the wood).
Any adjustment to the spring plate screws should be done a half/quarter turn at a time with the strings slackened; each time you make an adjustment you will need to retune the guitar and check the bridge.
This can be a tedious process, but i know from lifetime of using Floyd Rose equipped guitars that this effort is required to get the best out of the guitar. (Completely parallel might be a pain; as near as possible is good enough)
Assuming you intend to keep the same gauge strings on the guitar, once you have done this the first time, you shouldn't have to do it again when you change strings; unless something else major changes.
Edit: In your image - the distance of your strings from the pickup will also affect the tone of the guitar.