1. What kind of bonds exist between the metal and the carbene moiety in the Schrock type carbene complexes?

Two normal covalent interaction.

2. What kind of metal centers prefer the formation of the Fischer type carbene complexes? 

The late−transition metals having low valent oxidation state.

3. How does reactivity of the Fischer type and the Schrock type carbene complexes differ with regard to the attacks by electrophiles and nucleophiles?

Nucleophilic attack at the carbene−C center of the Fischer type complex and the electrophilic attack at the carbene−C center of the Schrock type complex.