Except you can actually take up to 4 attacks, assuming you hit with both initial attacks. see below.
No. It's three attacks. You get two attacks on a primary target, then a third attack on the primary (or another) target if you are wielding a particular weapon. That's it. There is no requirement for hitting with either of the first two attacks, or else the "make a secondary attack" qualifier would have been under the "Hit:" entry, not a "Weapon:" entry.
The "weapon" section of a power description modifies the immediately preceding "hit" "miss" or "effect" section (see silverstep for example).
No, it doesn't.
Therefore, the weapon section of Rain of Blows is a part of the "hit" section, which is applied each time the character hits with an attack roll indicated by the "Primary Attack" section. Thus, for each hit, someone with a light blade, spear or flail and at least 15 Dex gets a secondary attack.
No, it isn't. It's an entirely separate attack, unrelated to whether the primary attack(s) hit or not. If it was dependent on hitting, then "Make a secondary attack." would be under the "Hit:" section, just like every other power that requires you to hit to make a secondary attack.
The following powers all have secondary attacks that require you to hit with the primary attack in order to get a secondary attack. They all directly specify under the "Hit:" section that you must hit with the primary attack to gain the second attack.
Arc of the Righteous (67), Battle Pyres (74), Passing Attack (78), Giant's Wake (81), Fangs of Steel (84).
Giant’s Wake Fighter Attack 13
You lay about with heavy, sweeping blows, hewing your enemies left and right.
Encounter ✦ Martial,Weapon
Standard Action Melee weapon
Primary Target: One creature
Attack: Strength vs. AC
Hit: 2[W] + Strength modifier damage. Make a secondary attack.
Weapon: If you’re wielding an axe, you gain a bonus to the damage roll equal to your Constitution modifier.
Secondary Target: Each enemy adjacent to the primary target and within your melee reach
Secondary Attack: Strength vs. AC
Hit: 1[W] + Strength modifier damage.
Weapon: If you’re wielding an axe, you gain a bonus to the damage roll equal to your Constitution modifier.
The above is exactly how it's formatted when you are required to hit with your secondary attack. The qualifier is under the "Hit:" entry.
The following powers all have secondary attacks that do not require you to hit with the primary attack in order to get a secondary attack, as the requirement for the secondary attack is not specified under the "Hit:" section, but rather the "Effect:" or "Weapon:" section.
Rain of Blows (79), Devastation's Wake (84), Cruel Reaper (85), Weaponsoul Dance (87).
Rain of Blows Fighter Attack 3
You become a blur of motion, raining a series of blows upon your opponent.
Encounter ✦ Martial, Weapon
Standard Action Melee weapon
Primary Target: One creature
Attack: Strength vs. AC, two attacks
Hit: 1[W] + Strength modifier damage.
Weapon: If you’re wielding a light blade, a spear, or a flail and have Dexterity 15 or higher, make a secondary attack.
Secondary Target: The same or a different target
Secondary Attack: Strength vs. AC
Hit: 1[W] + Strength modifier damage.
The above is exactly how it's formatted when you don't need to hit to gain the secondary attack, because the qualifier is under the "Weapon:" entry and only requires you to be wielding a particular type of weapon.
Yeah, it's perfectly clear. You get two attacks against one target. If you have the right weapon, you get a third attack, against any target within range.