Yes you CAN cut the coils then weld them to the buckets. I have done this on 2wd (lowered) trucks. You get a 2/4" drop for around $100. But, I have never or would ever do it on something that would ever go into the mud. There are many differences between how a lowered ride and a stock ride truck are treated and what you can get away with.
You need to simply buy smaller coils. Rent/borrow a spring compressor remove your old and put in the smaller ones. You may need to pull one to find out what the spring rate/company is before ordering if you want a similar ride to what you have now.
Yes dropping it 3" is going to change your steering linkage. Without knowing what pittman arm you have now who knows. Putting a different one in is not hard.
Now before you do all this stuff. Go out there and turn the wheel all the way to the right look at the wheel well/frame. Then do it to the other side. Are you going to have clearance issues with your current tire/rim combo once it is lowered? Just from looking at the photo you may need to trim your bumper a bit so it does not hit on hard ruts.