There's an extensive paragraph describing the damage calculation on the wiki.
The short version is: multiplicatively with weights.
The slightly-less-short version is: armor adds its own multipliers on top of health's multiplier (cumulatively) and reduces damage the health takes. However,
- the more armor the enemy has, the more weight armor's multiplier has over health's multiplier,
- damage types strong against armor reduce that protection (dealing more damage), while damage types weak against armor increase that protection (dealing less damage) - on top of the damage multiplier.
(Copied from my answer to a similar, but much broader, question.)
Forgive me if I'm off topic of your question but this is how I can think to answer your oddly phrased question.
According to the wiki:
Killing an enemy with a warframe ability (molecular prime) will grant 100% of the experience from each enemy killed to your warframe. If you use weapons, it splits the experience 50/50 between your warframe and weapon.
When you're playing co-op and an ally kills an enemy, the experience gained is equally divided between your frame and each weapon.
According to personal experience:
When I first started playing warframe I had my friend explain the experience mechanics to me. He was probably completely wrong but it actually does make sense. He's told me that when you kill an enemy with an ability/weapon, you get 100% of the total experience toward your correlating weapon/frame, and then it divides the experience between your other gear. This CAN NOT be 100% correct (since I've never actually levelled a secondary by using my primaries) but I don't think hes too far off of the actual answer.
In all this leads me to believe that, when you kill an enemy with an ability, it gives you 100% of that total experience to your frame and then an additional bonus to your weapons. In regards to your "leeching method", its an inaccurate test according to this:
Kills: You get a bonus 50% experience from all kills at the end of mission.
If you want an accurate comparison, multiply your experience from the kill run by 2/3 (100% + 50% = 150% total, 2/3 of this would be 100%).
Best Answer
Syndicates are far less formally bonding than you have been told - it comes down to a few things.
Faction Sigils
The easiest way to gain reputation with a faction (Syndicate) is to equip their Sigil on your Warframe, and gain XP. For every 30xp (might need to check this) gained, you gain 1 reputation with that faction - and with the higher level sigils, you will gain a slightly higher amount (up to +15%).
You get the initial faction sigils from the initial offering to a faction, and you can do this initial offering for all of the factions with no negative penalty.
Daily Missions
After the second offering for a given faction, you will get three missions available that refresh at Midnight (UTC). These offer a fixed amount of reputation for completion, and don't count towards you daily reputation cap.
Negative Reputation
The reason you might have thought you can only be in one faction at a time is possibly due to the Allied / Enemy system - some factions 'dislike' each other, and gaining positive reputation with one will give you negative reputation with another.
In practice, this means that you can probably expect to keep three factions happy, and be hated by the other three.
TL;DR
You can level any syndicate by simply wearing their sigil, which you get by making the initial payment - you'll get dailies to do after another level. There's nothing keeping you to a single syndicate bar common sense.
Hope that helps.