1. Yes, there is a difference. 'Too' means an excess , or more than is good or healthy.
For example, you can say 'My problem is that I'm too fond of chocolate' . This means that you like chocolate such a lot that you eat too much of it, and that you are perhaps putting on weight as a result.
2. To 'be fond of' means to 'have an affection for'. With regard to a person, it is a feeling stronger than 'like' but not as strong as 'love'. You can also be fond of things. This suggests a very personal preference, which, as in the case of the chocolate example, may be excessive.