Plant id help required for our garden

[Fraxinus]

I have spent today finishing off tidying up the garden around our cottage walls and have yet to tackle the strip along the drive and have two plants I can't id from my books.
The first is almost like a Barberry (Berberis vulgaris) but the leaves don't quite look right, pics of leaves and flowers then branch.

the other is a complete unknown to me

if anyone can id these that would be great.
Thanks in advance for any insight.

Rob.

 

[Mesquite]

The top one is a berberis for sure... possibly darwinii

Bottom one I recognise but damned if I can remember the name

 

[slowworm]

Bottom pic is a geranium of some sort.

 

[Fraxinus]

The top one is a berberis for sure... possibly darwinii

Bottom one I recognise but damned if I can remember the name

Darwinii is the closest match in my book, but the artists drawing had spikier leaves which got me confuddled, so thank you for your prompt clarification.

Bottom pic is a geranium of some sort.

cheers, going to give my google-fu a workout to see how to stop it being so invasive.

Rob.