As you can see there is a connector screwed to coil pack. Some small black box and some connector. My female part of connector fall apart and as you can see male part is cracked too. I broth other one from you pull that is in photo and have to cut wire to connect existing wire to new connector.
Can I drive without that thing. Is it good idea cut wire in engine bay and how is proper way to connect it?

 

So it is something called "radio ignition interference capacitor".
New Ford Lincoln Mercury Radio Ignition Interference Capacitor F6AZ 18801 A | eBay

 

Right, and it will cause no harm to drive without it .
Seems mostly for am radio.