I would add an automatic blood pressure monitor cuff - the kind you put on the arm and it measures it by itself. Buy one off the shelf and take it to your doctor the next time you go and check it's reading with the machine in the doctor's office. If yours does not register as the doctor's, adjust your thinking to make yours like it. As in, if yours is ten points higher than his, mentally take off ten points when you use yours. You need to know the blood pressure of your patient and that also gives the heart rate. You will know how to evaluate those two items if you get the book I mention below.
There are two airways in your kit. Don't use them if you have no training. I recommend buying an EMT training book as that will tell you how to use that and how to use an oxygen tank with mask. Do not use an oxygen tank with mask until you read that, as you could blow out the lungs of your patient.
I looked on Amazon and there is one EMT book that is $18.73. Name is “McGraw-Hill's EMT-Basic, Second Edition”. Just a first aid book will not have instruction in airways and oxygen tank use and information on heart rate and blood pressure.
I see you have a stethoscope. I recommend everyone have one. That is a fast way to determine if there is a heartbeat. Feeling for a pulse at the neck or wrist is too iffy to find in an emergency situation, especially if you aren't used to doing that. The stethoscope is for sure if the heart is beating or not.
I have two pairs of EMT shears and I don't use them - they are awkward and I think dull. I have a pair of Singer scissors that are sharp and will cut through the toughest material. The Singer scissors are years old but made when metal was serious metal, and made sharp.
If the SHTF, I will not be suturing up wounds. I think suturing is SHTF fairy tale talk - the pain would be too great for the patient. Will use Celox to stop the bleeding and plenty of Steri-Strips to hold the wound together. If it's a huge wound and should have stitches, and an emergency room is available, that's where I take the patient. Otherwise, the Celox and Steri-Strips is it. If an artery is cut, that's likely a death outcome shortly.
The best preventive to avoid serious accident in a SHTF situation, is, DON'T CLIMB. Falling from a height, can break limbs and cause head injury. Breaking a thigh bone (femur) can cut the femoral artery and that person will die as that artery is deep in the leg to protect it and you can't get to it and if you could, you can't stop the bleeding. With every heartbeat, the artery gushes blood. Don't climb yourself and don't let children climb.
If a head is bleeding, assume the skull is crushed there. Assume it so you won't put pressure there and shove a bone fragment into the brain. Use Celox to stop the bleeding and bandage carefully, not pushing on that spot.
In the EMT manual, you will see how to bandage different type wounds, including head wounds.
I would have to say, after learning to evaluate a patient and apply life saving techniques, two of my specialties in EMT training, was determining what the flow of oxygen needed to be from a tank and applying the right mask, and learning different bandaging techniques, including pressure bandages.