If one person, or 20,000 people are allowed to do it, why couldn't your spouse? The visa doesn't grant special privileges, it just identifies the reason for the visit.
Do not state the nature of the business, just the fact you work for the company in software development, your work is remote, you will not interact with any Thai companies or individuals. You'll need an employment certificate specifying those 3 points.
You apply at the immigration office that has jurisdiction over where your TM30 is filed so you won't be doing anything in Bangkok if you live in Lampu, possibly what they meant was that they send it to Bangkok for approval.