Port 80 is no different than any other port so far as being vulnerable to attack. Port 80 is best known for hosting http traffic, but you can do that on any port, and you can have any other program listen on port 80.

The attack vulnerabilities come in when you are running http traffic through port 80. The attacks are geared toward the "most likely" -- and the de facto standard for http / web traffic is port 80. So..choosing to run your FTP server on port 80 limits the kinds of attacks you will be subject to. Your FTP server will ignore all http requests.

So...that said your questions:
1) On your local computer, probably doesn't matter much. On your router, it can get sticky. If you're forwarding port 80 then whatever you're forwarding to needs to be inspecting the traffic it receives on that port. If your router hosts its admin function on port 80....well, I don't leave it there. I don't think that makes it any more vulnerable, just easier to find (so be SURE to change your default password).
2) According to Microsoft -- [url=http://msdn.microsoft.com/en-us/library/aa384291(VS.85).aspx:3aqw3pmm]Windows Remote Management is one component of the Windows Hardware Management features that manage server hardware locally and remotely.[/url:3aqw3pmm] ([url=http://www.blackviper.com/WinVista/Services/Windows_Remote_Management_(WS_Management).htm:3aqw3pmm]here's[/url:3aqw3pmm]a normal explanation) What this means....it allows your computer (with proper authentication) to be remotely managed.
3) Changing their status will prevent your computer from being remotely managed. Either by you from another network connected machine, by Microsoft during support calls (I imagine they use this, why else have it?) or by hackers (unlikely as your router should be blocking these requests anyway, but included for completeness). Worst case, you disallow it. Something stops working, you reallow it.
4) My philosophy is to secure the network as a whole, and keep most of the security from impacting the local desktop. My router and proxy server serve as the guardians of my network. They do all the filtering/firewalling/destruction necessary before my local computers even see the big bad internet. As such, I tend not to run firewalls at all on my home computers. Exceptions being laptops when they leave the house.
5) The only relation to the router is that if the router does not allow the traffic through, then the traffic will not get to the local computer. To hack your computer, you either have to initiate something (open an application that tunnels through the Internet via allowed paths), or someone has to hack your router first.

and that's a long post. :/ Sorry.

The best way I can think of to describe the relationship between router and computer is to equate it to a night club. Imagine your network as a nightclub, your computer as the open bar, and the router as the bouncer standing outside. Your bouncer has a list of everyone allowed into the nightclub from outside (VPN Tunneling), but ignores any and everything that goes on inside. He doesn't care. If you're in the nightclub, you're allowed to be there. If you're not, you have to be on his list. The bouncer's other list though, contains a list of publicly available drinks. Someone walks up to him, asks for a drink, if it's on the list you're served the drink. If it's not, you're escorted off the premises. (open ports on the router).

Inside the club, people can move about freely. The bar has a list of approved drinks (open ports on your computer). Anyone in the club can ask for any drink, only those on the approved list will get served. The bar can choose to allow everything and anything to the people in the nightclub, but instruct the bouncer to only serve one drink.

OK, the analogy breaks down easily, but I hope it simplified it for you.

The router should have an admin screen. I'd imagine it's where you set your password and there will be an option for remote Management. The IP address should be listed there.