Is there any way that I can download apps that I removed last week? (I can't remember the names of them)
If you've downloaded them on the Mac App Store. - You can find them again in the "Purchased" tab inside Mac App Store.
If you downloaded them outside of the Mac App Store. - They might be in your specified "Downloads" folder, if you haven't deleted them from that.
If you downloaded them on your iPhone/iPad. - You can find your previously purchased apps on these devices either on iTunes or in App Store on your device. Go to the "Updates" tab and choose "Purchased".