They're not checking it because it's associated with your passport and they see it as soon as they scan your passport. If it doesn't come up when they scan you passport, then you'll run into issues.
Yes, if you apply for a 1-year extension but your passport is not valid that long, then your extension will only last until your passport expires. Just know what that means for the future. Your new annual extension every year going forward will be in May, and you'll need to make sure your bank account is at the proper amount to apply for an extension in February or March since you'll be applying for your extension much earlier than normal the next time.
You didn't tell us what the visa is so we can't answer your question and tell you what is correct.
There's no such thing as renewing a visa. You can apply for an extension of stay. If based on marriage to Thai the requirement is 400,000 in a Thai bank account. For retirement the requirement is 800,000 in a Thai bank account. For a different type of visa, tell us what you're actually asking so we can answer you.
No. The only thing immigration office accepts is embassy certified income. The US embassy does not do this anymore for many years. So income is not an option for your first extension. You can use 12 months proof of monthly international transfers for subsequent years, but the first year will always be 800k in your Thai bank account.