yes. your c:\xampp\htdocs\abantecart_mantismoon\public_html is document root directory of web-server.
When you enable ftp for upgrading abantecart will try to find it. It's also looking for directories with those names like htdocs, www, public_html

abantecart upgrade package DO NOT change any custom data. Only core's and default template files
We are always recommend to users do full backup of your site (files + mysql dump) before upgrade.
If you want to upgrade to latest version I would recommend to wait a bit  and do upgrade to version 1.1.6 too that will be released soon.

it's a bug. Commit with all changed files  here
https://github.com/abantecart/abantecart-src/commit/0ecf6ef979ea42327f7bf1b7475b977cf40962a2
you can just replace old files by changed.
Note: bug fix is only for v1.1.5 and goes to version 1.1.6 that will be released soon

try to search word "maintenance" in admin

regarding dual boot. You do not have to. You can to create bootable usb-flash drive and tune all what you need there, i mean l.a.m.p..
But agreed to create a testcase for the OS, which differs from the OS of hosting provider it at least strange.
Windows is bad os for realtime tasks, especially vista.

could you try to set your document_root directory(root of webserver) as home directory for ftp user ?
We tune ftp mode for common cases, by another words, for hosting providers. As i see in filezilla log abantecart try to find your document root directory bu ftp-search and not found directory that  needed.

regarding backup error. it's automatic backup before upgrade but if user do full backup manually it's not needed. You can igrore.

Automatically - no.
I overview this stuff. I think you can convert it very quickly. On storefront side it's only model and language
On admin side i see only compounding  config.xml file that describe settings of extension and language.
You can download our developer tools and then create new with type shipping. It will generate folder with your extension_txt_id and structure...also config.xml and main.php file..
then you will only transfer model, languages, and build the config.xml.

slider is banner block. banner block have banner's. Every banner have image. look into menu design->banner manager

try to write

echo $orders['products']['sku'];

controller $this->data['orders'] become $orders variable inside tpl..