It's important to understand what the comma is actually doing here in order to know which side of the "and" it belongs on. In a sentence like this, there are only two possibilities.
1) Connecting two independent clauses with the help of a conjunction. In this case the conjunction belongs to the second clause, so the comma must come before it.
Clause 1: I couldn't see what was there.
Clause 2: I turned on the light.
Joined together: I couldn't see what was there, so I turned on the light.
2) Setting off a parenthetical element. This is an expansion of CarSmack's comment above. The commas will only be around the "extra information" in the sentence (the parenthetical element), so if "and" is part of the larger sentence you will see a comma after it. There will always be a second comma in the sentence if this is the function the first comma is serving.
Original sentence: I apologized to my father and to my mother as well.
Extra information: I was still angry at my mother.
Sentence with parenthetical element: I apologized to my father and, though I was still angry at her, to my mother as well.
I hope from these examples it's starting to become clear that in the sentence you provided there is no parenthetical element. Instead, two clauses are being joined using "and" as a conjunction.
Clause 1: Suggesting expressions are usually expressed when a subordinate makes a proposal or suggestion to the superior.
Clause 2: [Suggesting expressions are usually expressed] with sincere expressions.
Joined together: Suggesting expressions are usually expressed when a subordinate makes a proposal or suggestion to the superior, and usually with sincere expressions.
Sentence 1 is correct. Sentence 2 is not.
Note: As people in the comments have noted, the meaning of this sentence is quite confusing regardless of comma placement. It's hard to tell without context if it's actually worded poorly or if it's just a sentence that makes little sense alone.