Can I apply presets to videos in Lightroom?

"I just got the paid version 3.4 and my screen doesn't look like the screenshot here. I don't even see a library option at the top of my screen."

Sounds like you're using the cloudy version of Lightroom, not the traditional folders-based Lightroom Classic. (Shame on Adobe for such confusing product names.)  But you've posted in the forum for Lightroom Classic -- if you repost in the cloudy Lightroom forum, you'll likely get an answer quickly:

https://community.adobe.com/t5/lightroom/bd-p/lightroom?page=1&sort=latest_replies&filter=all 

[Use the blue reply button under the first post to ensure replies sort properly.]

You can apply a develop preset to one or more videos using the Quick Develop panel on the right side of Library:

You can also apply basic adjustments to exposure and white balance.

But beware that video in LR has never been well-supported by Adobe.  Many people complain about frequent bugs, stuttering playback, inability to correctly import basic metadata like capture date, lack of support for common codecs (e.g. HEVC/H.265 on Windows), lack of basic features such as rotating videos, and limited abilities to export into other formats.

Some good info here: https://www.lightroompresets.com/blogs/pretty-presets-blog/116015684-video-editing-in-lightroom-how-to-apply-your-favorite-pretty-presets-to-video

That might be enough to get you what you want. For higher-end work, check the Creative tools here: Video editing software, video editor for Mac and PC | Adobe