You have to select what you want to group, right click, and make it a group. That'll make it a sub-object in the heirarchy. Components are different - basically they allow you to copy one subobject over and over and when you edit one of them, it edits all of the others. As for the program; it's powerful, but you have to just hide some of the more complex mesh parts when you're working. It's a downside, but worth it IMO.
If anyone here needs help with using Sketchup for making game models, I've got experience with it, I can help you

Also, another word of warning - all those little greebles should be made into subobjects before you export (you can make the greebles one object). The reason being is that when you draw on a face and then push/pull it out, you're basically drawing an extrusion, which eats up polies like you wouldn't believe. When you group them and remake the face without the extrusion, it saves lots of polies.