What’s the best way to store potatoes and maximize their shelf-life

It depends on what type of lettuce it is -- part of the issue is that if the lettuce is touching plastic, it will rot quicker, so I wrap it in paper towels, then bag it (but not sealed), and keep it in my crisper.

For whole heads of lettuce (iceburg, butter, red leaf, etc), I just wrap the whole thing in dry paper towels, then shove it back into the bag from the grocery store or farmer's market. I then pull off leaves as I need it, and re-wrap it. It stores for well over a week this way.

For mescalin mixes, arugula, or other individual leaves, I'll wash them, dry them, then unroll enough paper towels to spread the leaves on, then roll up the whole thing, and bag the roll (again, not sealed), and keep it in my crisper. I can probably get a week out of it this way.

(all times assume you're not buying from a store where it's been sitting on the shelf too long before you buy it; I get my lettuce when I can from the local farmer's market)

So, to answer the specific questions:

• keep the bag open; you don't want moisture to condense inside the bag, as it'll make the lettuce rot faster.
• I get better storage time with heads of letuce keeping them whole. If you're going to be eating it all within 2-3 days, it probably doesn't matter, and for loose lettuce, I find it more convenient to wash it as I re-pack it anyway.
• You never want to store lettuce wet ... you might be able to store it completely submerged, but damp will lead to it rotting faster.

To store fats, you should always use glass as plastics react to fats by absorbing some and perhaps discoloring or transferring flavors to your fat. Depending on use, I prefer to work with cold fat at the start as it has a much broader possible use and I don't like to wait when I make biscuits, so I keep mine in the fridge. However, you gain very little extra life out of keeping it in the fridge and if you don't keep it in a sealed container you run a very real risk of flavor transference there to. If you don't make pastry dough or other such, your counter top is a perfectly acceptable place to store, as long as you use it up before it goes rancid. One thing to keep in mind is that fats can sometimes have very different shelf lives, so make sure you taste or smell before use, regardless of storage method.