2 Answers

It depends on the purpose of your fast... Religious or health reasons?
For health reasons - It depends on the reasons for your fast, weight loss? cleansing and detoxing? etc. An absolute fast does not allow the a person to eat or drink anything at all, but this kind of fast MUST not be longer than 24 hours.
The purpose of fasting (other than religious reasons) is systematic cleansing of the body. During a fast the body will cleanse its self of everything except vital tissues. The deepness of the cleanse depends on the type and duration of fast.
There are several types of fasting other than absolute fasting. These are; water fasting, juice fasting and fruit fasting.
Water fasting only allows the intake of water and nothing else. It is a very intense form of fasting but because of this is has a higher rate of detoxifying and healing. You can water fast for a maximum of 40 days, with an experienced faster supervising you.
Juice fasting involves a person consuming just raw fruit and vegetable juices along with water. These foods require little energy to pass through the digestion process. They are thought to be a good source of vitamins and antioxidants.
Fruit fasting is a less intense form of fasting. Its a great option for weight loss, especially for those would like a healthy diet whilst quickly loosing weight. Fruit fasting drastically lowers the body fat intakes whilst still providing all the nutrients your body requires.

No. Fasting is not eating anything, including ice cream.