Is it possible to trim or adjust video content in InDesign's Media panel?

Not within the Media panel of InDesign, but have you considered Photoshop? I'll bet you already know much about Photoshop, but many forget that it also can edit video. When you have a CC license, you likely have all the big Adobe apps. David C. recommends the video editing software, and I do, too. But in a pinch, Photoshop will do!

I don't think so, however you probably don't want to trim it there anyway. Trimming does not alter the original video, so depending on how much you trim the download time would not be improved. Better to trim it off in Premiere Pro or Adobe Media Encoder and make a copy. (Media Encoder only trims from the heads & tails; it cannot cut out parts from the middle.)

For cheap and cheerful video editing have a look at Adobe Express. It may not be Premiere Pro but it will do for simple jobs, and it's easy to learn how to use it (and it's free!)

I've had great success adding donwloaded videos directly in Indesign using the Media feature, exporting to PDF and playing seamleessly with full control in PDF. For client presenting video storyboards it works great. I've moved completely out of Keynote and into Indesign for presenting and supplying video embedded presentation to clients now because the tech works so well. I haven't managed to be able to trim the vid yet, but I'm on the hunt for that ability as well. 🙂

Interactive PDF is a horrible format for multimedia; in fact, beyond simple navigation and specialized forms, where you can control the read application, it is nothing short of a crapshoot.

You can't successfully include a video in an Interactive PDF, you can include a hyperlink to an external video source, such as a YouTube video. Alternatively use another format based on HTML5  such as InDesign's Publish Online, FXL ePub or In5, that's an InDesign plugin (at extra cost).

To edit a video use Photoshop or Premiere Pro.