Learn English – Starting a sentence with “Starting with”

To (also in order to, having the same meaning as in order that and so that) in each of those sentences is a subordinating conjunction, which is what begins a dependent clause. The comma is not necessary between the two clauses, but (as FumbleFingers says) it is preferred when it improves readability, which is usually when the first clause is rather long.

In your examples, I would prefer the comma.

The comma isn’t so much a dangerous weapon as an easily blunted scalpel.

Whatever pointing practice you follow, mechanical or rhetorical, using too many commas tends to blur the significance of each. So while FumbleFingers is exactly correct in suggesting that a comma before as applicable marks the natural pause you take in speech before adding this qualification to what has gone before, its significance is confused by the presence of all those other commas which serve a different purpose.

I suggest instead that a more readable solution would be to mark this phrase with different points—it might be parentheses, it might be dashes—and that you place the parenthesis before the list, to avoid distressing your readers by implying that their applications will be defective if they fail to include the names of maiden aunts they don’t have:

In your application, please include (as applicable) your telephone number, cell phone number, e-mail address, names of maiden aunts, and a list of schools you have attended.

(And if it wuz me I’d do something to clarify the scope of that your, which at present gives the impression of including (your) names... and (your) list..., too. But once I start rewriting I find it hard to stop.)