London Parks & Gardens Trust aims to increase knowledge and appreciation of parks, squares, community gardens, cemeteries, churchyards - all those places that form London's open space network.<span>Trust members - amateurs and professionals - provide and enjoy lectures, walks, day trips, children's programmes, a newsletter and journal, research and an inventory of historic green spaces.</span>
Не везде понятен смысл, но попробую догадаться. Я бы внёс такие правки:
Young officer Almazov wanted to enter the Academy and to serve in the regiment. Professor at the Academy rejected job (painting, может быть, если подходит по смыслу? речь идёт не о написанном сочинении, а о написанной картине? если так, то written не подойдёт) by the officer. Almazov made a mistake - he painted a bush absent in reality.
<span>Officer's wife found out about the situation and helped her husband. Vera sold all her jewelry and paid the gardener who planted a lilac bush. Almazov showed professor the bush, an so the officer managed to enter the Academy.</span>
<span>Mildred’s out <u>going on </u>some errands; do you want to wait for her?</span>
Милдред отъехала по каким-то поручениям, не хотите подождать ее?
также возможно to tun errand - быть на побегушках и to do errand - выполнять поручение, но мне кажется to go on an errand - пойти (поехать) по поручению, здесь подходит больше всего
