Work on core and squat to improve gym strength

I have noticed a drop in my strength in weight lifting esp bench press. Previously I had focused on back  muscles to improve strength and that helped and I need to continue to do that. But i have neglected my core, I just do crunch and lower back, that is only 2 out of 5 core muscle group and also for those two i don't do a lot. I need to make my core and full squat stronger to increase my weight lifting. For the core I need to focus on all 5 core muscle groups.  The core exercises i need to do are :

1. Transverse Abdominis (TVA)  muscles are the belt like muscle that wraps like a belt. Exercises: Planks
2. External Obliques are the muscles on side and front of the ab around the waist. Exercises: Arm twist
3. Internal Obliques are the muscles under the external obliques and in opposite direction to them. Exercises: Cross over crunches 
4. Rectus Abdominis (Six pack) runs along front of the abs. Exercises: Crunch
5. Erector Spinae (lower back) is a muscle that runs from neck to lower back. Exercise: back extension

Additional muscles not traditionally core but neglected and important are : 

• gluts and side hips
• hip flexors which are part of pelvis and upper thigh
• hip abductors which are medial thigh