“The teacher came to class and advised the students.” Is this sentence simple or compound. Argument for simple is it contains singular subject

OP's usage was common enough a century or two ago, but today you'd normally only find for being used to mean because in deliberately archaic/poetic contexts...

Lord, help me for I am poor and alone.

My guess is it's impossible to recast OP's exact words into a "simple" sentence (whatever that means), because semantically there are effectively two separate elements...

We forgive our enemies
[So/Therefore, please/you should] forgive me

You can only recast it into more modern English - "We forgive our enemies, so you should forgive me".

As has been pointed out, perhaps what OP actually means is "Forgive me in the same way that we forgive our enemies". Because the sentiment itself has "dated" religious overtones of The Lord's Prayer ("Forgive us our trespasses as we forgive those that trespass against us"), it's not a good example to "modernise". But in general we tend to use like in such constructions today...

"I just wish you could love me like I love you" (where as would be somewhat dated/poetic today).

It's also worth pointing out that as = because could be used in my first example, but my feeling is that in general we tend to avoid using as with either of those senses today. Or if we do, we tend to use other "devices" to make the meaning clearer...

1: "As you said you wouldn't be home until late, I only cooked tea for myself"
2: "I only cooked tea for myself as you said you wouldn't be home until late"

Putting as at the start in #1 makes it "stand out" more, so it's easier to parse/interpret (but probably most speakers would use since or because anyway).

3: "I only cooked tea for myself, just as I usually do on Tuesday nights when you work late"

Including just also helps the usage stand out - again, making it easier to parse (but many speakers today would use like there, even though others may consider such usage "slangy").

You have parsed this correctly: in the final sentence the verb and the ‘heavy’ conjunct subject are flipped so that the ‘lighter’ predicate is first and the ‘new information’ falls at the end of the sentence.