Actually, I'm really surprised they got permission from all the sports leagues to use their trademarks and not have to put some small print in crediting them. You don't get to use the Premier League logo, for example, without a licence.
(to answer your second point, I've done a lot of work in the sports area, so use of league and team logos is something I'm fairly up on).
I'm really surprised as well, as several of those leagues do not allow sportsbooks to use their logos, especially the MLB, which has had several betting scandals in the past.
The NFL also do not grant license requests to use its logo to sportsbook; only certain business partners (and their subsidiaries) may use the NFL logo in association with a sportsbook offering.
(to answer your second point, I've done a lot of work in the sports area, so use of league and team logos is something I'm fairly up on).