I'm having lower back pain and I'm feeling unstable sometimes when bending or even when walking, I feel like my back just gives out?

Try conditioning. Sounds like there may be some muscular weakness in your back. Try going to your family md for eval and a referral to physical therapy to strengthen your low back or look for reasons for instability.
Several options. If you have not tried core exercises to strengthen your back (tummy and back muscles), try that first. Regular aerobic exercise is also important. If you still feel unstable, see a spine specialist for examination and assessment.
That's a problem. When you have a problem with your lower back its not unusual to have your leg feel like its not there or to give out on you. If you irritate a nerve its like flipping a switch and cutting the power to your leg - it goes right out. It can be caused by a slipped disc, arthritis, or instability between two adjacent levels. It probably needs to be evaluated with an MRI to see what's going on.