2. You need at least 1 type of defense on the ship for defense assists to work. Likewise, you need 1 type of attack on a ship for attack assist to work. If your ship has 0 defense, defense assist will do nothing for it. Same for attack assists. If you hold the mouse over the ship's stats on the main galaxy screen you can get a popup that shows what bonuses your ships are getting from nearby starbases.
4. Some techs, like Impulse Drive, increase your speed ability, which may be why you see this extra boost in speed. Since you said it was early in the game, that would be my best guess since, depending on your starting techs, it doesn't take too long to get to Impulse Drive.