In regards to question 1: This depends on the location of the actual tear, the outer third of the meniscus is relatively vascularized resulting in a greater potential to heal. The inner 2/3 of the meniscus is relatively avascular diminishing its regenerative properties. Typically labeling a meniscus as being a complex tear implies injury extending into the inner 2/3.
Surgery is generally not required unless a person experiences persistent swelling and/or instability and dysfunction.
In regards to lifting, squatting below parallel may cause you irritation as forces acting on the meniscus increase with increased knee flexion, you may want to squat at 90 degrees and above, again this has great individual variation and you may be just fine going below and you as a person need to do a risk-reward analysis. Dead-lifting inherently requires less knee flexion so I do not anticipate you having problems with d/l. You may have to make adjustments as far as frequency and volume to your program.