When signing a type A free agent, a signing team with an amatuer draft pick lower than 16th pick loses their 2nd round pick instead of 1st round,.is this corrrct?
That is correct, though it's important to understand that it's the first 16 "natural" picks that are protected, i.e. non Type D picks. So if there is a Type D among those first 16 picks, then it's actually the first 17 picks that are protected. If there are multiple Type D's, then adjust accordingly.
Also, if the same team in the example above signed multiple type A free agents...is their 1st round draft choice still retained? If so what other pIcks are lost with the subsequent type A signings (if sucessful)
Subsequent Type A signings will just lose their next natural pick. So in your example, they lose their second round pick by signing their first Type A, they'll lose their third round pick if they sign a second Type A, etc.