There's also a scruffy looking hedge at the front that we thought was
completely dead at first. From looking round the local garden centre,
I think it might be a Potentilla (Goldfinger?) - some yellow flowers
are just starting to come out.

What's the best way to look after it? It looks like it needs a good
trim & is quite thin and scrawny at the base of each stem in the
hedge, but I'm not sure how, or when.