You sure know the right questions to ask. MANY books have been written dealing with the repercussions of these 2 questions. One reason for this is that a little bit of knowledge formerly led us to incorrect conclusions. I will try to simply lots of physiologic research controversy.
1) Can training little girls this age increase endurance - yes but...
As children grow their lung capacity grows (until around age 20). Short term training does not appear to increase endurance, however long term training (years) does seem to have significant effects. This effect may be due to better technique - child athletes develop more economical breathing patterns. By age 16 training effects and difference between athletes and couch veggies is quite marked. While a good training program can increase a child's aerobic fitness on the order of 10%, apparently adults can make bigger gains more easily.
2) Can weight training prior to puberty/skeletal maturity damage joints and connective tissue?
Children are very prone to overuse injuries around their joints. Possible explanations are that their bodies aren't ready for such stresses, they are too eager to please adults (just say no), inadequate stretching and nutritional factors (especially problematic among female athletes). Repeating the same activity over and over again leads to pain and ultimately to serious injuries if the child's activity is not adjusted. We have a good deal of evidence that lifting weights does not significantly build muscle mass in prepubertal children. Certainly lifting weights that feel heavy is risky to the child. So why do it? Well the evidence is that lifting weights, if performed correctly, does lead to strength increases and possibly prevent injuries. Although the muscles aren't getting bigger the child's body learns to efficiently coordinate the work of the muscles and perform more effectively. So weight lifting is a good idea but with light weights and close attention to properly controlled technique.
I see these questions as a physician as I see them as a soccer coach. That is establishing proper technique is crucially important in young athletes. Learning to strike the ball well can really annoy a big boy who can hit it hard already but he won't look so hot when every shot goes straight at the keeper or over the goal because he didn't learn the proper technique. You can't get hung up on the outcome in children - more goals or faster sprint times. Those achievements come as years pass. That foundation pays massive dividends as the child matures IF THE CHILD STILL LOVES THE GAME!
My chief concern is the very real risk of pushing the children too hard and killing their love of the game. As a physician I preach the paramount importance of lifelong physical activity. It absolutely crushes me when I see children injured or growing to hate any sport (especially my beloved soccer) because for them it was turned into a job instead of a game by a well-intentioned adult. The line is very thin between being a coach who offers his/her players everything they need to realize their potential and the coach who makes the players work so hard they hate the sport and you. The greatest youth coaches find ways to blend having fun and challenging the players in just the right measures.
There are many good sources of information
Children's Sports Training by Jozef Drabik - Stadion Publishing, Vermont 1996.
and Tudor Bompa's books are good for coaches and parents.
Human Kinetics is the biggest publisher in sports medicine and so an excellent resource. The American College of Sports Medicine and American Academy of Pediatrics publish expert opinion statements relevant to child athletics.
Michael Carlston, M.D.