Is it correct to say:
I worked at a software company and I would sell different programs.
To me, would does not sound appropriate here for past habits.
Is selling considered a state like work or live?
Would doesn't sound completely right here, because usually sentences with would (meaning a habit) imply a trigger or a condition. For example
Every time my alarm rang, I would put it on snooze. (alarm = trigger)
Whenever my mom was in the room, I would pretend to be doing homework. (mom was in the room = trigger)
So I don't think
*I worked at a software company and I would sell different programs.
Used to strongly implies a habit that is no longer going on. But then you would probably use it in the first clause:
I used to work at a software company and sell different programs.
*I worked at a software company and used to sell different programs.
The latter is technically correct, but implies that working at a software company and having sold programs have nothing to do with each other.
The most natural way to convey what you're trying to convey is the simplest:
I worked at a software company and sold different programs.
I thought it might have to do wuth the fact that selling programs was an expected part of the job, a normal state of affairs. She argued that it was a repeated action in the past. It simply did not sound right to me as a native speaker and I wished to explain why.
IMO your thinking was correct as to a normal state of affairs. As a past form of will, would evokes a sense of elected (voluntary) action, as opposed to simply fulfilling the requirements of the job. Consider the difference in the following sentence:
"At lunch, Jane would sit with her friends, but in class, she sat (aka had to sit, was seated, etc.) next to her nemesis."
Here, the inclusion of would in the first clause says that Jane frequently chose to sit with her friends, whereas its exclusion in the second clause takes Jane's wishes out of the picture. Seats were assigned, so she had no choice.
Used to, on the other hand, is not identical to would, in that it clearly closes the possibility that Jane continue to sit with her friends:
"At lunch, Jane used to sit with her friends" relegates this behavior to the past, whether it be that Jane, these friendships, or the possibility of having lunch together no longer exist.
Put another way, "I used to smoke" says that I no longer do, whereas the recollection that "I would drink and smoke too much" not only leaves open the possibility that I drink and smoke now but also carries a tinge of self-recrimination, in that I chose to do these things for better or worse.
As for states, such as "I used to love that" or "We used to be friends" would is logically excluded in the past, precisely because a state cannot be an act of one's will. A state simply is (or was).
"Would" is fine, from a grammar point of view, but sounds a little odd: a little archaic perhaps. As @FumbleFingers says, it would be better to simply write "..and I sold different programs".
I don't understand quite what you're asking about "selling" vs "work or live" and what the relevance is to this question.
To refer to past habits which you no longer practise, you can use "used to" with state and action verbs (no restrictions) whereas "would" can only be used with action verbs.