there is absolutely nothing stopping you from entering from a different country than where the visa was issued. You could have an itinerary through multiple countries. But they require you to be present in the country you apply in.
told you what it actually happening, based on personal reports from people going through it. They want you to be present in the country of application until the visa is issued, and if they find that you are not, they will likely cancel the application without refund. That many people have done it without "getting caught" doesn't mean that is the way to do it. Just for example in Laos they require you to come pay at the embassy in person. Pretty sure that's to make sure you are in Laos and not trying to apply from somewhere else.
Did you already use the 60 day visit family extension based on being married? That extension is available once per entry. And it would allow you to both buy time to season your money, and also lets you apply again directly for the one year extension, without needing to start over with a new initial 90 day non o.
oh.. I didn't know that possibility existed. Always just read that no.. You cant get a visa off of your (half thai) children if they are older than 20. Must be a rare case if the half Thai children support their foreign parent economically for a visa.
A parent cannot be dependent on a child for visa purposes. It's the other way around. You can get a visa for being the parent of a Thai child, until the child is 20 years. When the child is older than that, there are no visas available based on that child anymore.
the choice to only allow cash payment is probably not about them not having the means to receive money digitally or otherwise. I suspect it's more about making sure you are actually in Laos and not trying to apply while being in Thailand.
you should anyway also get a letter from the school stating you are a student there and that they have granted leave for the trip. That could smooth things over if questioned. Any decent school will provide such a letter for accepted leave.
no you can't stay a long time on a tourist visa or visa exempt. That's why people get refused entry when doing that. If you want to stay for a long time, then you need an appropriate visa.