Best way to increase morale is winning. if you're not fighting then you have to buy new clothes and change often but afaik until guys have 2 fights their morale shouldn't drop like that. anyway, on "Possessions" page there is a number next to the clothes you purchased. brand new clothes are 150 and they drop 2 points every day. some guys change'em everyday, some once it gets to 142, some even lower.
also on Possessions page if you hover over your fighters' name it will show their exact morale (don't know how to do to it on mobile). if you do the same thing on your gym page, or if you click the scale on the top right of your fighters' profile page, it will show their exact energy level.
without VIP, the only way to find out how many people are in sparring sessions is to look at "sparring schedule" link on your gym's page.