Is it true that long length at birth is an indicator of height later in life?

No. This is one I have never heard before, but i can tell you that it is very hard to predict adult height, especially at birth. The best way to "estimate" adult height is still based on the parents' heights and family history. Nutrition also plays a big role in ultimate adult height, as does the timing of puberty.
No. Babies are born to fit their mothers womb. This has nothing to do with their final height. Their final height has to do with their genetics and diet. Height at birth can also be affected by mother's diet during pregnancy and whether or not she smoked during the pregnancy. These things can make the baby shorter at birth.