Is it true that i'll shrink in height as part of my discs will be removed?

No. We all lose 2 iches with age as our disc collapse there is no height loss with disc removal you would notice.
Perhaps. If you are having a diskectomy without anything else, you may lose a fraction of an inch, not enough to notice. If a fusion is done or deformity is corrected (as in scoliosis correction), you may actually get a gain in height (which may or may not be noticeable.