He just proved sage mode can be released anytime the user wants. Minato is a perfect sage, he surpassed Jiraya in everything including sage mode. Obviously minato can maintain it for more than 15 seconds, he wouldn't be a perfect sage if he couldn't.No, because he was too busy making Naruto with Kushina and cooking her dinner. It's all speculation on your part. I'm backed up with manga scans.
He does have Perfect TSM but it isn't longer than Naruto's, it hasn't been shown.
Even if it was shorter than Naruto's he has FTG to make full use of it.