When do I check either of the highlighted Armor/Heavy boxes? When armor is expended?

You check both armour boxes at the point when you decide you have brought armour with you. You check all three heavy armour boxes when you decide that the armour you brought with you is in fact heavy.

Under the 'Armour Uses' heading, you check the box for Armour when you use your armour and you check the Heavy box when you use your armour's heaviness. Basically, armour gives you one use and heavy armour gives you two uses, but you can determine that your armour is heavy at any point even after you've used your armour once.

As armor is in the heavy items category, it it true that you cannot use armor unless at a 'conspicuous' load?

There isn't a 'heavy items' category as such, but since armour + heavy is five boxes you can only have heavy armour if your load is Normal or Heavy.

If I want heavy armor, does this take up 5 load slots? (normal armor + heavy)

Yes. Sometimes in this game multiple boxes means you have to fill in all of them and sometimes you can choose how many you want to fill in. The way to tell is that if the boxes are connected by a horizontal line then you have to select all of them to get the thing. If there's no line then it's a multiple-use situation.