How do the stats convert into a percental value?

They don't, because you have to take in account the target's stats for the opposing stats. Unless we can data mine the enemies and get every single one's stats, and you can make an add-on to show these variables when in battle with that specific enemy (Which, by the way, would be considered cheating to be honest, since it could work in PVP theoretically.)

Parry by the way was changed in Heavensward so that it no longer is raised by Strength and Dexterity.

These are known as statweights.

Typically they are expressed as a ratio of how much X stat (SS, Crit, Det) is worth in Main Stat (STR/VIT/DEX/INT). For example Crit is weighted at 0.387, so it takes around 2.6 crit on your gear to be equal to a point of STR or DEX.

Dervy is one of the people who crunches out the stat weights for us (thanks) using mathematical models: https://dervyxiv.wordpress.com/stat-weights/

Ariyala's Toolkit: http://ffxiv.ariyala.com/ has a gear calculator that uses the statweights to find out what's the best stuff to wear.

For "toughness" it's pretty much how much VIT you have in practice.

For healing, it's mostly preference, but I've found that no one stat is more important than the others. There's a maximum of piety that you want (a little, not a lot).

For endgame raiding, you're looking at your DPS output for all classes rather than your ability to tank or heal, since you don't need a lot of toughness or healing throughput in order to actually do it.