Posted: 10/03/2016 at 21:19
I think the hedge was probably planted for privacy from next door and you would be quite overlooked if you got rid of it.
I'm still not sure which side gets shade and which gets sun. Is the fence in shade? If you want flowers and colour then dig up some lawn in a sunny bit, add some compost and plant some flowering perennials, such as salvias, lupins, pinks, campanula, rudbeckia, penstemon etc. If it is a shady place then go for shade loving plants with colour and/or form in the leaves, such as hosta, heuchera, Brunnera "Jack Frost, certain hardy geraniums, pulmonarias.
Is the fence in shade? It would look nice with a bit of trellis along the top for a bit more height and wires fixed along it to support climbers. But the climbers you choose would have to like it, so if it's shady you are more limited. There are clematis to suit most situations. I would enlarge the bed it front. I like curved lines in gardens rather than squares and straight lines, so I would make the corners of the lawn rounded. But it's your garden so you choose, depending on what you like.
Is the brick terrace bit in shade or sun? Is it big enough for seating and some pots of flowers, or herbs?
If you want to know about gardens or gardening it helps to buy a book and do research using Google.