Is it possible to combine active and passive gems of different colors

Levelling up a gem is like levelling up a skill in many other games. It gives you higher damage, more effects, higher requirements, etc.

As you can see, burning arrow gains 3% physical damage, and 1% greater chance to ignite enemies. It also now requires you to be level 2 to use it.

I believe higher levels of Raise Zombie increase zombie health and damage. For other (non-summon) skills, the stats of the new level were shown on the gem at one point during beta, but do not appear to be shown now. The reason minion statistics aren't shown on the skill is because they don't exist on the skill, they exist on the minion.

Mark_GGG on the forums says

(Minion statistical information) isn't hidden, it doesn't exist. Ideally we'd like to make it exist and be visible eventually, but this a) requires implementing entirely new systems for skills to be able to show stats that aren't in the skill, and b) requires those stats having actual values we can read somewhere. We've got a temporary solution for Zombie life numbers, which need updating any time any balance changes modify what those values are, but it's simply not viable to make that a large-scale solution.

You get more zombies from the passive tree.

There is a penalty for some levels delta, indeed:

There is a penalty to the chance of currency items (scrolls, orbs, etc.) dropping in areas with a monster level more than two levels lower than your character level. For each additional level that you have compared to the area's monster level+2, the chance of a currency item drop is reduced by 2.5%.

So if you are level 30 in a level 20 area, you will see 20% less currency item drops on average: 2.5*(30-(20+2))=20

A level 30 character in a level 28 area will see no penalty.

Source: http://en.pathofexilewiki.com/wiki/Drop_Rate

The way I understand it: there is a penalty for currency items only, therefore nothing for other items.