I do have one question can I put all the LEDs, the fet and the other IC on the same heatsink?
Yes, but only if you isolate them. The drain on the MOSFET (were the LED connects in the schematic) is connected to the metal tab. Since I don't know your LEDs I cannot say if one of their pins connects to any conducting material the heatsink will come in touch with.
The other IC is... What?
You can get some heat conducting, electrically isolating washers for a TO-220 and if the LED has got any exposed parts towards the heatsink, I guess whoever sold the LEDs should have some that fits the LEDs.
When mounting the MOSFET, use an isolating bushing made for the purpose - then the screw won't short them (or use nylon screws).
The heatsink should be rated for the total power it sees (and calculate with an ambient temperature of ~40°C (it's the air right next to the heatsink). Any higher and touching it may be less pleasant.