Going through the points;

Coup-de-grace

Coup-de-grace does not specify if the victim makes any noise if they fail their Fortitude save of 10+damage dealt (and thus die) however if they make the save then they certainly would wake up.

This then becomes a DM decision. I personally would make a second Fortitude save for the monster against the same DC with a modifier of the characters stealth bonus rather than the +10, which takes into account how good the character is. If this is failed then the victim expires noisily, this then gives others nearby a chance to hear/wake up.

Waking giants

The DC to use perception when asleep is +10, meaning a base DC of 20 to wake if they are asleep, modified - as you say - by noise of the weapon, once battle starts this is -10, which means a DC 0 to wake up.

Note: There is a lot of debate about battle at waking up on the pazio forums

If the giants wake up then they will be effectively flat footed and surprised for a round, the round thereafter they would roll initiative as normal and remain flatfooted until their go.

Stealing from giants

Stealing a small item from a sleeping giants body will be sleight of hand DC 20, the giant gets a penalty to detect this as they're asleep (+10). Stealing larger objects should, as you say, give a bigger penalty (although not covered directly by the rules). If the bag of loot is merely beside the giant then stealth should be used instead and the giant again makes a perception roll vs. this.

The standard coin weighs about a third of an ounce (50 to the pound).

Sizes and weights of monsters are listed here which gives you the weight of an person for small of "8-60 lbs" quite a lot really! But there's no weight modifier for objects as these are related to the size of the creature that is using it - ie a large sized dagger or small sized dagger for the creature wielding. Just a weight modifier for armour. (about three quarters down, "armour for unusual sizes")

This means it's down to your call; I'd scale it up with multiple -2 penalties for every 10 lbs they're trying to lift, which is 500 coins as they're more likely to clink clink clink.

Passive skills (especially perception, but anything really), are representative of a sort of "always on" ability. So, for instance, if you're walking in a forest and there is a goblin ambush, you see them if your passive perception beats their stealth score. However, if you're specifically looking for ambushes, you'll roll it actively.

So in the secret doors case, when you walk into a room, if your passive perception is high enough to spot the secret door, you notice it. If you're specifically looking for a secret door, then you roll an active check to try to notice (naturally, if you roll less than 10, you don't learn anything new).

Generally, the only time to roll an active perception check is if you are looking for something that your passive perception did not pick up. Naturally, in the course of play this happens fairly regularly. But the passive skills are designed to reflect a characters natural competence and should be used when they are sufficient, or there is no particular rush.