Solved Moss IDs please

My darling daughter decided that I wanted a bonsai, so on my birthday, guess what I got. OK. So I now had something new to learn about.
When it arrived the chinese elm was growing in coir peat - yuck!! (Have to repot) - in a small plastic training pot(?), in a chinese style outer container (undrained).
Chinese elm are, apparently, repotted in spring.
Leaf buds started to burst so it is now repotted in bonsai compost, in a new bonsai container.
I decided I needed moss on the soil.
Moss 01
Lifted from the base of a tree, and suspect it won't like full sun.


Moss 02
A lump of moss that fell from the roofing tiles. Should like sun.


Moss 03

Collected from concrete steps out the back. Probably same as #02


This was near to #03, but very wet and fell to bits. Again I suspect same as #03.


I'm still studying Common mosses on walls - British Bryological Society. but the more brains the better.

So, any ideas, guys?

TIA

Fof

EDIT: All have been pressed down to enhance contact, so they may be a bit squashed.

 

Looks like the stuff that grows on my shed roof and in the gutters, I'm afraid moss is mostly moss to me.
Apart from sphagnum.

 

The top one looks like Polytrichium, used a lot by the Japanese for moss lawns.
If you can find a copy 'Moss Gardening@ by George Schenk is well worth a read, and some beautiful pictures. My copy says printed in 1999 but you may get hold of a second hand copy.

 

Our house roof is covered with this moss. It eventually lands on the patio or in the gutters. Not sure if the magpies remove it or it dries out and springs off. Lots of the stuff. I'm always sweeping it up.

 

Know little about mosses (yet) but confirm chunks are slung out of gutters by magpies. Its the only thing they do thats useful!
What I would like to know is whether the Chinese Elm will tolerate the dampness that mosses require ?

 

@infradig
I know most mosses require moist shady conditions, which wouldn't be optimal for an indoor bonsai, grown on a SW facing window sill.
I know there are mosses that can, and do, thrive on roofs, walls etc that can be exposed to extended periods of full sun and very little moisture.
I have seen images of bonsai with moss covered soil, so I'm just experimenting. I expect to have to mist the moss to keep it green, without watering the tree.