First, use the right kind of shrimp. Either buy fresh, wild caught shrimp (pricey) or buy frozen, uncooked wild caught shrimp THAT DOES NOT HAVE PRESERVATIVES! May be hard to find in some areas, but it is available. The preservatives, number one, are not good for your body; and, number two, turn the shrimp into mush (Cook's Illustrated tested frozen shrimp a while back, cannot remember issue date) and proved this theory.
Another thing to be aware of, especially to those with anti-biotic allergies, is the possible contamination of farm raised shellfish with anti-biotics. Believe me, I learned my lesson the HARD WAY! I am allergic to penicillin and we went to the local Big Boy on a Friday for the all-u-can eat seafood buffet and ate the shrimp cocktail. WHAMO-allergic reaction! I suffered for 2 weeks! Asked manager and sure enough, the shrimp were farmed. I no longer eat seafood off of buffets!
Another thing, refrain from using previously cooked shrimp. You might as well throw a couple of rubberbands in the soup!
And yes, the shrimp will continue to cook after you put them in the soup. I dare say, you may want to get the soup up to simmer and toss in the shrimp (thaw first if using frozen) just prior to serving. Just take off of the heat and leave covered for approx. 3 minutes and you should be good to go!
As far as undercooked shrimp, that would depend on the quality of the shrimp to begin with.
Hope this helps! Warm regards,
Lori