mushrooms and purslane

My husband called me outside to see these interesting mushrooms that came up around the mailbox.

Never seen anything like them. Very pale with hints of yellow-green.

Because of them I was looking closely at things in that patch, and saw that my flowering purslane here is producing seed. The seeds are in these little cups

I started collecting them, tipping out into a tupperware.

This one you can see the cap on the seed cup starting to come off.

They are very very tiny and gray, wrinkled texture. I tried to find out more about saving flowering purslane seed- I want to know if I plant these next year, will I get more plants with the same color flowers or will they revert to another form.

But all the info I found online about purslane seed is for the common purslane grown as a food item- the leaves and stems are edible, so are the seeds I found out. Some people collect them en masse- uprooting the plants and sifting the seeds out over a screen. Those seeds are black. Are mine gray because it's a decorative variety of plant? not sure.

I'm saving as many seed as I can so I can grow more of this in other parts of the yard next year. I bet a lot crop up on their own around the mailbox, so I could always just transplant them too.