Many people are able to time their sale and purchase so they happen on the same "closing date". As a buyer, you can make your offer "conditional" on the sale of your existing home, so you're not paying for the upkeep of two homes. Or when selling, you can try to extend the "closing period" to give yourself more time to find your next home.
The sale of the severed portion of vacant land would not be subject to GST/HST since it is not capital property used primarily (more than 50%) in a business and it is not being sold in the course of a business. However, if the land was subdivided into more than two parts, sales of the severed portions are not exempt unless the portion is sold to a relative (or to a former spouse or common-law partner) for their personal use.