The "approval" bonus tiles are "morale" bonus tiles.  They double (since they're all 100%) the effect of any "morale" building placed on them.

"Happiness" is simply the sum of all your approval pluses (buildings, racial bonuses, etc) and minuses (taxes, population, etc).

Technically "approval" itself is a direct modification to (a planet's) morale, unmodified by the population modifier (which is a multiplier, so it drags everything down).  The only instance in the game at present of this is the 10% bonus for having a planet of PQ 11 or higher (greater than PQ 10).  However, at one time (apparently) the Neutral ethical bonus was a straight approval bonus rather than morale, and the Secret Police Center is supposed to be a straight approval bonus (theoretically, at least), but at present is bugged and only does morale instead, hence making it useless.

At the end of all of this, your approval on a planetary basis is averaged via your population and then determines your civ-wide approval.  Basically what this means is that it's okay to have some of your less populous worlds less happy than some of your more populous worlds-but this doesn't happen terribly often, as the mechanics of approval itself tend to counterbalance that effect.

The wiki has more info.

I was always under the impression that popularity was how well the other races viewed you, but I never looked into it in any great detail, so I could be wrong.  Even assuming that is the case, I'm unaware if minor races count towards that or not.

Just what I needed to know especially the

Ah, the popularity graph.  It is, indeed, a measure of how well liked each race is.  If you have a mostly peaceful galaxy, then bribe a whole bunch of races to go to war, you can see their popularity drop like a rock while yours skyrockets.  It basically assigns a value to each relation level (At War, Hostile, Wary, Cool, Neutral, Warm, Friendly, Close, Ally, Team) and totals them up to get the popularity values.  I don't know if minors are included in the calculation, or the exact number values for each relationship level.