Some mysteries to solve...

My truck was in the garage, I went to Auckland for 24 hours and there was stuff to take care of with my father so I hadn't worked since last Wednesday. I'd intended to go JNKs but there was a car in the way of where I need to back the truck in so today I stopped in and asked if they could move it sometime. Of course they were very happy to do that and I was able to do two loads until even my yellow safety glasses weren't bright enough for me to see anymore. I was going to dump the second load because I have a big day tomorrow but when I had to turn my headlights on, I realised I really did just have to stop!
Which I did. Outside the legendary Lobster Pot. I hadn't been in there since I was a kid but instead of ordering a piece of fish, I got Shrimp Chowmein. It felt like such a treat after a couple of hours of sawing dead branches and scraping up wandering dew.

This time you need to keep an eye on the Nikau (?) in the very middle to get a sense of the changes (that's the scruffy one you see in the top two).
When I trimmed it last week, it had one open frond and one tightly shut so it was a real reward to see this tonight...

Now to the mysteries...I'm the first to admit that a) I never know what I'm doing and just go by instincts and b) this means I don't know many plants.
So I found a virtual miniture forest under these trees today. All of them had baby ones of the themselves coming up all around them and I felt mean ripping them out but I could tell by their parents that it wasn't wise to leave them there. BUT I also didn't know which ones to keep for planting elsewhere either. I'd sooo appreciate your help by first telling me if the above plant is actually a Nikau or something else then by identifying the below three plants and tell me the pro's and con's for keeping/relocating or greenwasting them. I get a sense they might be natives but that for every one I've pulled out, 3 will soon appear in it's place - especially now there is light and air around them...