Cute questions! Our daughter was not one to allow barrettes or headbands when she was young and I hated when her hair was in her eyes. So I always kept her bangs trimmed. When the length was looking a little straggly, I would very slightly trim the ends so there was a nice line at the bottom. But I'm a former hair stylist, so there ya go! It's almost like I just couldn't keep my hands off it, really.
On the flip side, my SIL let her daughter's hair just grow and grow. It looks good now at 6 yo, but probably didn't look good until she was about 4 yo. And yes, it did look straggly to me. There's really no right or wrong, it's just a personal preference. (And no, there is no truth to 'cutting it now will make it grow in thicker.' However, when hair has a nice trim at the bottom, it does appear to be thicker than if you have various lengths going at once)
At 6, now our daughter has all one length, long hair. It was a bugger to grow those bangs out, but she did need them when she was a baby/toddler.
Finally, I always put the tights over the diaper, then the onesie over the tights.