As I mentioned in the comments, you're looking at the wrong aspect of armor. You shouldn't be looking at the percentage it reduces, but rather the amount of damage it actually prevents as a measure of how much longer that armor lets your survive.
Let's consider an example for a champion with 0 armor. Say he has 1000 health, just 'cause that's a nice round number. Now our champion gets caught in Garen's judgement, and starts taking 100 physical damage each second (at one hit per second). Clearly, our protagonist can take ten hits before dying.
But now, imagine our champion has the 50 armor you mention, meaning the incoming physical damage is reduced. Now (still with 1000 health) it takes 15 seconds for that bastard Garen to claim our champion's life. 50 armor extended our life by 5 seconds. (100 * (2/3) = 66.6 DPS; 1000 / 66.66... = 15 hits)
So our champion respawns, wises up, and buys 50 more armor. Now with 100 armor, we're sitting at a flat 50% damage reduction. Again we run into Garen, who's still dealing 100 base damage per second. It now takes him twice as long to kill us -- 20 seconds. Once again the armor has extended our life, again by 5 seconds. (100 * .5 = 50 DPS; 1000 / 50 = 20 hits)
Back in base, we buy another 50 armor. We're now at 150 armor, and 60% damage reduction. Enter Garen -- spinspinspinspinspinspin and it takes 25 seconds before our champion dies. Again, adding 50 armor extended our life by 5 seconds. (100 * .4 = 40 DPS; 1000 / 40 = 25 hits)
So even while the amount of damage reduced per point of armor diminishes (as you observed), the amount of time armor extends your life (or effective health) remains distinctly linear.
Each item slot, 1-6, is initially bound to the corresponding number key.
You can rebind this during gameplay if you wish, but I like to simply move activated items into the 2nd slot and hit 2.
Best Answer
Using the actives of items takes a lot of practice and there is no "do that and you will use the actives more often"
However, there are tipps I can give to you which make it some kind of a habit to use them:
Assign them always to the same hotkey
When building items, always try to assing them to the same slot depending on the champion. This makes your brain think they are just another skill for e certain champion.
What I like to do is use QWER for my normal skills, 1 2 3 4 for my active items, T for my trinket, 5 for items that place Stealthwards and 6 for Vision Wards.
Muscle memory is a huge factor when it come to LoL, especially with skills and actives.
You can drag items to the slot you want by holding down the left mousebutton when hovering them, drag them over the slot you want and release the mousebutton. You often have to drag the items a little away from your inventory to make the drag animation appear.
Always keep an eye on their cooldown
Its the same thing like looking on the map now and then to see whats going on, looking at your R cooldown or at the timers for baron and dragon. "Just" add your Item slots to your screen-looking-rotation and you will remind yourself of the items you have.
Replace champion skills that are just passives
Bind your Blade of the ruined King on Vayne to her W, as it is only a passive, it will perfectly fit on her kit, and will feel just like a normal spell. (thanks to shunwoo for this tipp)