I just moved into a new town home and these plants are outside. I do not know what they are and how I should I care for them. Should I prune them back etc.
Welcome to your new home.
From the photo, plant number 1 in the black container with the twigs appears to be dogwood. Cornus is a genus with 30-60 species of woody plants, which are distinguished by their blossoms, berries and distinctive bark. Dogwoods like to be exposed to morning sunlight but protected from the hot afternoons. Keep the soil moist at all times but don’t let it become soggy. Containerized trees dry out quickly so be sure to check the soil daily especially during hot, dry summers. A mulch will help reserve moisture and keep the soil cool. You can feed your dogwood monthly during spring and summer, using a water based fertilizer. If you choose to, you can feed the tree using a time release fertilizer every three months. The following web sites will provide useful information.
Plant #2 is a rhododendron.
Rhododendrons have long been mainstays of late spring because of its spectacular clusters of showy blooms and large green leaves that often last through winter. The flowers are usually tubular-, funnel-, or bell-shaped—and often fragrant. The leaves for the smaller azalea are usually pointed and narrow; the leaves of the rhododendron are generally large and leathery.
This shrub generally performs best if provided with moisture and some shelter. They prefer climates with adequate rainfall and moist summers. The rhododendron can be fussy, preferring environments where it is neither too hot nor too cold (Zones 5 to 8). They need a certain amount of chilling to develop strong flower buds. Most large-leaved varieties require dappled shade; avoid deep shade or full sun. A sunny spot that receives a few hours of shade is perfect. Soil should be well-drained, humus-rich, moist, and acidic (pH 4.5–6). Amend planting areas with compost, peat moss, or a substitute, and oak leaves to achieve ideal conditions. Mulch plants annually with 2 to 5 inches of pine bark chips or pine needles to protect shallow roots, retain soil moisture, and keep the soil damp. A lack of water reduces flower-bud formation. (Keep mulch a few inches away from the trunk.) Make sure you keep your rhododendron well watered until the soil freezes.
After flowering, deadhead where practical, to promote vegetative growth rather than seed production.According to the American Rhododendrum Society, “If a plant grows out over a walk or needs to be restricted for some reason, it may be pruned back moderately without fear that the plant as a whole will be damaged. It is often possible to do this pruning during the blooming season and have flowers for the house. Old leggy plants may need pruning, but often these are better replaced with smaller newer varieties. Old plants, however, can be cut back severely and still recover, although it may be a while before they bloom again.”
Here are two web sites which are great resources for information on this plant.