Do units receive a defensive bonus when you select "Do nothing" or hit space?

No they don't, this unit simply didn't take a turn - with the exception that the unit is stationed on a tile that provides a defensive bonus (for example a fortress) or they're on rough terrain.

A full list of conditions and bonuses as well as base statistics for each unit type is detailed in this article. Of particular note is the following;

• +25% defensive bonus for rough terrain (hills, forest or jungle)
• -10% defensive penalty for open terrain (not hill, forest or jungle)
• +20-40% defensive bonus for unit Fortification. The fortifying unit gains +20% on the first turn, and +40% thereafter