Should I worry that my baby is not always at the same percentile on the growth chart?

Not sure. The way babies are measured in their pcp's office can be a problem sometimes particularly if the "paper and pencil" method is used. Babies squirm and this method is highly inaccurate. An infantometer is the gold standard for measuring a baby's length.
Keep a watch. Babies can shift percentiles over first 2 years of life but needs to monitored by your pcp.
No. Babies often switch curves on a growth chart, depending on their activity levels, the time of day the measurement is taken, and the genetic potential for growth they are given by her parents. As long as your baby continues to grow, the growth curves are just guides.
Maybe. Certainly babies and kids will alter growth percentiles at times throughout growth. For instance, when a child goes from sitting to crawling and walking, their weight percentile can dip due to a huge increase in activity without eating much more. However, large changes in any growth parameter can be an issue. Talk it over with your doc and look at the curves with them to make sure things are ok.