Looks like Queen Anne style to me. The back is called a vasiform splat. ie. it looks like a vase. HTH

Something like silver birch trees don't take up too much room but will provide some height and interest. Personally I pick out natives, after asking local garden centres for those which are natural to my area. I've used black mondo grass across the front of my walls with purple fountain grass behind it. The fountain grass really takes the summer heat, doesn't need much water and self-seeds. It's grown slightly taller than me after a few years. I have, what I call a 'survival of the fittest' garden. Over the years, I've experimented with all sorts of plants. Eventually, only those that survive with little help, and almost no extraneous watering, get to stay. One of the key things I did when planting out my garden was to dig down into the soil and lay a mat of used, natural-blend carpet underlay (not the more synthetic types used these days). Just ask someone getting rid of their old carpet- it's easy to come across. Above the carpet underlay I added water crystals, then put the soil back on top. After the gardens have been established, I haven't need to get the hose out since. I do have lots of succulents around the place, some native plants and ornamental grasses. I hope this helps.

It looks like it's one of the Alocasia, Colocasia group of plants. There are many varieties and your local nursery will be able to help you.

I agree with Jabinika that it doesn't look great just now. However if storage is an issue its a wasted space, and should be put to work. It looks as though many things are not yet finished. With lots of light paintwork and some aesthetically pleasing storage boxes, I feel it will do well. It would be good to see a pic of it complete.