If you buy an item that is on sale in play store, and remove it from your device, can you still reinstall it at a later time?
Yes... I do this all the time when apps/games I might like come up for sale cheap or free, or major titles I might use someday, although they don't have to be on sale. In fact, I often don't even let them install and cancel the download. They are always in your apps list or "Library" as it seems to be called now, to be installed later.
Once you have purchased an app, regardless if it is on sale or not, or whether you actually install it or not, the license (and thus the future rights to install the app), are tied to the Google account you used when you purchased the app. As long as you use the same Google account, you can reinstall the app to the same or any compatible device that is connected to the Google account you used to make the purchase.
You will notice if you have paid for an app that it will appear in your list or searches with an Install button instead of a "price" or purchase button, you can click it and select the device you wish to install it on without paying again.