Probably the best alternative to Premier is KdenLive or DaVinci.
As for After Effects, I’m not too sure. The alternatives definitely exist, I’m just not sure which one to recommend. It’s been years since I’ve done any compositing. But I use KdenLive for video editing regularly and it’s great.
In fact, the past year of development has been monumental in the amount of improvements and new features.
@CeeBee Also you mentioned compositing, the industry standard is Linux compatible and has a free trial too, Nuke.