Some beginner questions on attacking and assualting.

[Liebchen]

You asked: 5. Does terrain effect the attacker at all? If I shoot from the high ground would it do more damage than being level or below a enemy formation?

During an assault (not fire), the attacker gains the benefits of the defender's terrain, since the assault is understood to be occurring in their hex.
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You asked: 7. Besides a reduction in fire & LOS, what else does elevation do?

With regard to LOS, being on a higher elevation does allow a unit to see over many obstacles - including other units.
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You asked: 5. I see that some tank formations are able to shoot from more than one hex away. How big is the drop in effectiveness?

The amount that fire effectiveness is reduced is defined for each scenario in the parameter table (hit "F4" to see it). It is often something like 1/2 or 1/3 effective, but don't hold me to it, because scenario designers do what they feel fits best for the scenario.
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You asked: 1. Does ZOC extent hex bordering terrain? Like rivers, streams and embankments and stuff.

Consider ZOC to be a product of the units' fire effectiveness, as well as possibly patrols.
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You asked: 4. Likewise, can I somehow manually refresh the spotting of enemy formations? If I can move one troop to a high ground position and have LOS over a chunk of the battle, is there any way I can save the remaining movement points rather than let them go to waste and end the turn?

Some units are "recon" units. You may spend 1/3 of their MP on a spotting action. You'll find this command in the "Command" menu, if you've highlighted the unit. Use this, and there is a "chance" that enemy units within LOS of the recon unit will be spotted. Sometimes they're identified and sometimes they're mystery units. And sometimes they're not shown, too.

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You really ought to take the time to read the user manual. Hit "f2" to get it. It's very well laid out, has searchability, and I find myself looking at it for refreshers often enough, even after 15 years of play. I'm not saying that you haven't read it, only that it is always worth re-reviewing.