"Well then, I'm leaving."
I think in an earlier exercise, it's shown that あの (a-no) is more of a filler word like how we would say "Um".
The example for that was あの、すみません (ano, sumimasen) (Um, excuse me).
From what I remember reading from the comments, では (pronounced de-wa in this case I think) is just a more formal way of saying "well then" whereas じゃあ was less formal, and for us more like "welp".
I'm still learning myself, so I'm more than willing to know if I'm wrong with this.
I thought 行ってきます was [I'll leave and then return]?
you are correct, duo's sentence is just translating a phrasal sentence into another phrasal sentence from English. In Japanese when you are going out of your home you say to your family 行ってきます "I'll leave and then return" and in English you can say "I'm leaving", to let then know you are on your way out. They are very similar but not in a literal way.
行ってきます is basically just いく + くる connected by the te-form in a polite tone. 行く → 行って +来る ～いってくる → いってき～ +ます→ 行ってきます。
As for the rest....
If you wanted to say "I'm going" in English, there are 2 meanings, the first is that you are going as a certain fact, for example:
A: Are you going to the party tomorrow? B: Yes, I'm going.
In that case, in Japanese you can just use「はい、行きます」。
The other case is when you are in the middle of going ("I'm going right now"), in Japanese, this is phrased differently, like:
「向かっている途中です」"I'm on my way (there)" or "I'm in the middle of heading there".
In the case of「行っています」it doesn't mean "I'm going" but is more like "(X) is in the state of having gone", for example「母はスーパーに行っています」"Mom has gone to the supermarket".
And if you wanted to say "I'm leaving" (let's say you were with a group and somehow wanted to express you are leaving for the day), in Japanese there are a number of ways to do this, but 失礼します "If you excuse me" and 帰ります "I'll return (to my home)" are very used.
Have you thought about applying to be a contributor Keith? How often do your suggestions get accepted? I submit about 10 a day and haven't had an email in months saying any were accepted. Sure some are probably wrong but I know most aren't.
(I just submitted さあ, 行ってきます- "さあ" seems a pretty reasonable approximation to "well then" in this context)
I was actually thinking about applying for a contributor but I am just not sure if I can contribute the time.
However for your question whether the suggestions get accepted or not, there was a reply in this post from one of the contributors => https://forum.duolingo.com/comment/38591435. It is quite tedious for a contributor to "accept" an answer so that the email is sent, so most of the times answers just got added without being "accepted" (by clicking a button in the system UI for each of the suggestions).