Base power is how powerful the move is. For example, in theory Earthquake will do more damage than Flash Cannon. It can be modified by weather, type effectiveness, STAB, certain moves, terrain, certain items, abilities, format (like Earthquake in double battles), and specific circumstances. However, base power does not guarantee a certain amount of damage inflicted on the target. That’s a combination of the stats of both Pokémon. For example, if you were to use Earthquake with a Modest nature Heatran with 0 Attack EVs, it wouldn’t do very much damage to, let’s say, a 252 HP and 252 Defense Bold Amoonguss. Heatran has low base Attack and it has an Attack lowering nature, while Amoonguss is fully invested in Defense and has a Defense boosting nature.
As for Giga Drain > Solar Beam, the only time Solar Beam is more viable is on sun teams, where it doesn’t have to charge. Giga Drain is much more practical because it doesn’t need to charge and it heals the user.
No one uses Cut except for an HM slave.
Note that there are some moves, like Dragon Rage (40 HP) that take a set amount of HP from the target.
Hope this helps! :)