how fast should a plant grow?

You're doing a multitude of things wrong....

1. You want a neutral soil or soiless mix. You can try promix or seedling starting soil that has no nutrients in it. This is essential.

2. You MUST know the PH of your water.. and never feed with rain water. It contains many metals it picks up from the atmosphere and is rich in nitrogen. Which is not good for a young seedling. You wouldn't think it to be so, but it's true. your seedling has all the nutrition it needs inside itself for the first 3 to 4 weeks.

3. You're bringing your plant in and out. Honestly pick one and stick with it. while this isn't necessarily harming your plant; it's not helping it either.

You're nearly a month into your grow and your plant looks like it's 1 week old with some severe stretching. I would start over and start again after I gained a solid knowledge base.

FYI: don't post plant problems in here. You should take it to the plant problems forums. I will not respond to anymore replies you post. We have a plant problems section specifically for this reason and you will get MUCH MORE help there.