More ID please!

I have done a bit of furtive googling with these things and not managed to come up with anything that looks like them...! Does anyone have any idea what these plants/weeds are and if I should keep them?


This is growing all over the lawn at the bottom of the garden. Very small white flowers and hairy stem. It looks quite dainty, but is this something a bit not good? I have no idea what it might be!



These things are growing in the bottom bit of the garden where the soil is quite muddy and wet. Is the grass a large kind of grass? Is the flower related to the grassy type thing? Also, are the leafy things on the left hand side anything nice to keep or something horrid and need to go?

Thank you so much for your help in advance... I have absolutely no idea what most plants are and am a complete novice...! Thank you again!!

 

The 1st one is Hairy Bittercress, spreads seeds everywhere.
The leaves on the left of the second pic. are Lesser celendine, Ranunculus ficaria as is the yellow flower again this spreads everywhere.

 

Celandine is now called Ficaria verna, by the way.