1.If we have many principal components (eg more than 5), all having eigen values more than one. Can we reduce the data in to two principal components intentionally?
2. Can we consider a variable as independent if it has strong loadings on two or more than two components?
1.- Yes you can, and even you can measure de "information" that you lose as the average squared projection error between your information after PCA projection and your information before PCA projection.
(you can see details in https://www.coursera.org/learn/machine-learning/home/welcome) week8/applying PCA/ choosing the number of principal components.
on the other hand, I recommend you normalize your data in order to get eigen values = 1.
2.- I don't understand what you mean with "strong loadings".
I hope it helps you.
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