Herschel, Doug correctly answered your question about folders "On My Mac". Following are my replies to your question, using corresponding numbers.
1) Mailplane (and Kiwi) use the "actual" Gmail interface via either the Safari webkit in the case of Mailplane or the Chrome webkit in the case of Kiwi. What you see in either app is "EXACTLY" what you see in the Gmail app itself. Everything...every single feature, including Settings, Contacts, Google+, whatever you use, are identical.
2) All the folders on your Mac that are synched from Gmail are going to already be in either Mailplane or Kiwi since they both use the "actual" Gmail app, only it's displayed within their own app UI...but in the very same visual format. Doug's reply addresses any folders you have in "On My Mac" as opposed to folders from Gmail displaying in your Gmail account in Apple Mail.
3) Do not delete Apple Mail. Simply delete your Gmail account from Apple Mail. If you keep the account, it will continue to cause synching problems in Gmail.
4) It will be...same with Kiwi. I think you should install both these on your computer so you'll see what I'm talking about...they both are the same Gmail interface as you are used to seeing and all your Gmail content will be displayed perfectly in either app. Mailplane has a 14-day trial period with an uncrippled version and Kiwi has a Lite version that is ad-supported in the MAS, but you'll still get the idea...just picture it without the ads after you pay the $10. Mailplane must be downloaded and purchased from http://mailplaneapp.com.
5) I honestly don't miss any features of Apple Mail, other than I do like the interface, probably because I've been in the computing industry for so many decades I'm used to standard email apps. Others may have different opinions, but if anything, I think I gain back features that Mail.app doesn't have, such as the ability to attach PDFs and images (big issue for me), rather than force me to insert them inline. Apple Mail is more like what we all have come to think an email client looks like over the years, while Mailplane and Kiwi are duplicates of Gmail, only with many added features, like the ability to use multiple Gmail accounts, and other Gmail add-on apps like Rapportive, etc.
6) Mailplane can be used on any Mac used by "you" and with "your" email addresses. If you want to install Mailplane on any other Mac a family member uses, you must purchase their family license which is for five Macs in your household. I have Mailplane on two Macs and my wife's.
Hope this helps. I'm not pushing either product, I'm simply tired of fighting this situation which will never get better.