Welcome - you know that Geno is happy to have coaches attend practices - he likes to pass on his knowledge, so if you ever are in the area during the basketball year, you can contact the athletic department and see if you can mesh your schedule. You are obviously a very perceptive person both about the uconn coaching staff and about the qualities exhibited by the posters on this forum!!!
To your questions:
The college schedule has a lot of gaps in contact periods, so there is not that much overlap of commitments. Because of the USA commitments, they have over the last 7+ years condensed some of the recruiting activity into periods where Geno is available - pushing for recruits to visit earlier or later, scheduling home visits, and viewing around the USA activities. The USA gig carries a certain cachet and exposure (as if Geno needed that!) so there is probably a pretty even balance between pluses and minuses - nothing like saying to a recruit 'I really am sorry I can't watch your AAU performance, but maybe you can catch some of the Olympic team game that evening and watch me instead!'
The staff has been given the option of being involved in various aspects of the National Team trials, practices, and competitions and have generally jumped at the chances. CD and Jen (Hartford HC and a former Uconn great) have both functioned as court coaches and advanced scouts and Shea and Marisa have done court coaching and leg work as well. It is I think seen as a great privilege by all of them to be involved and it is a benefit to the USA team. Not sure of what beyond expenses are involved in terms of compensation, but all expenses paid trips to the Olympics or WCs can't be bad! I suspect that they will all be in Rio, but would not be surprised if either Shea or Marisa or both remained in the USA depending on specific schedules and responsibilities regarding the Uconn program.
Because the players for the NT have such limited availability, the scheduling of NT duties is much less burdensome than it was pre professional options. Tara took a year off from Stanford for her gig, because that team was formed and training for 12 months prior to the games - they played 30 or something exhibitions and friendlies during that year. But there was no WNBA and very few US players played overseas in 1995-6.