As a German Native and historian, I apologize for any language mistakes and wrong vocab, but I hope I'm able to answer your question nonetheless. I do hope my answer is sufficient, if not, please ask more questions, so I know what you would like to know.

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After freeing the first camps, the American Army and Russian Red Army fed its survivors with anything they had - they had very good intentions. They soon realized that many of those inmates died from being "overfed" after being starved by the Nazis for so long. "Overfed" is set in quotation marks because it wasn't technically overfeeding, but the former inmates' digestive system had basically completely shut down as a result of the malnutrition (*1). Due to those experiences, the armies started to slowly increase the rations of all survivors they came across. The soups they cooked where alike the one the Nazis had given them, but a little thicker and with more vegetables. Thereby, the digestive system slowly started to work again better and better, until the survivors where finally able to "really" eat again (*3). They also managed to get the Polish Red Cross to distribute vitamin pills to Auschwitz survivors to help lessen the pain and health problems after the months-long malnutrition(*2). Survivors, who suffered from dehydration received hypodermic injections of water if they had any muscular mass left. All survivors were helped until they were healthy enough and decided to leave the caring facilities.

You also asked about the long term affects on the health of holocaust survivors. As far as I know, there are no actual statistics about the long term affects of living in a camp. I never came across one, and I just did another research and could not find any. The only statistics to be found are about psychiatric disorders. Here's a brief outline. The outline suggests that holocaust survivors appear to have a higher life expectancy compared to anyone else, which can be considered a long term affect. Based on my experience there are several reasons, why there are no actual statistics about the long term health issues of holocaust survivors:

• Medically speaking, it is very difficult to tell if certain health issues were caused simply by age, genetics or solely caused or 'just enabled' by the person's time in a camp.
• You have likely heard about Dr. Mengele before, who 'researched' by making human experiments with camp inmates. I am not sure that it would have been 'socially' acceptable for other doctors after the war to research what health issues the concentration camp caused. I am neither sure that former inmates would have wanted to know that health issue X was solely caused by their time in the camp, because it would have meant they were in a way still mistreated by Nazis on a daily basis and would be constantly reminded of the camp. From a psychological point of view that would have made coping even more difficult.
• Research shows that health issues of Holocaust survivors caused by the persecution was (on average) not investigated until 26 years after the persecution had ended. (*4) Thus, any statistics that may be available are likely insufficient.

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Sources:

Unfortunately, almost all sources I can offer are in German. I do not know if they have been officially translated, but Google Translate may help you out here. I assume there are a lot more sources in German than English, as the majority of the Holocaust victims were of German origin and wrote or told their experiences in German after the war.

*1 This is a witness report from Yehuda Bacon.

*2 Susanne Beyer, Martin Doerry: "Mich hat Auschwitz nie verlassen«: Überlebende des Konzentrationslagers berichten" ("'Auschwitz never left me': reports of survivors of the death camp"), page 4. --> Google books edition

*3 One of the English sources I found that you might like to look at is the United States Holocaust Memorial Museum's website. There are plenty of eye-witness reports there. The following videos answer part of your question:

• Report of Pat Lynch, US nurse who served during the liberation of concentration camps in Europe
• Report of Colonel Richard Seibel, US soldier during liberation of the Mauthausen camp.

*4 Martina Vees: "Die Begutachtung verfolgungsbedingter Störungen von Holocaustüberlebenden im Rahmen von Verschlimmerungsanträgen", p. 76. --> eBook edition