No. Blocking a contact does not delete previous text messages or call history. The old messages will remain on your phone until you manually delete the conversation thread.
Alternatively, you can swipe left on a contact in the blocked list and tap . where to find blocked contacts iphone
Yes. If a blocked number calls you, they will not get through, but they can still leave a voicemail. However, that voicemail is automatically sorted into a "Blocked Messages" folder at the bottom of your Voicemail list, so you won't get a notification for it. they will not get through