1. Yes you can use RealVNC from
www.realvnc.com and their are some variants that branched from this project. I dont know if WinVNC is one of those variants or not but if so then WinVNC and RealVNC should be compatitable.
2. Well Samba is what you want to use for that. A lot of new people and even not so new people always seem to have trouble setting up samba.
I suggest after initial install to get SWAT up and running by editing the /etc/inet.d and finding the line that has to do with SWAT. The line is commented out with a #, just remove the # and save the file.
Either reboot the computer or restart the inet daemon by typing
killall -HUP inetd
then you can open a web browser and go to this address
http://localhost:901/
It will prompt for the username and password. Type in root as the username and whatever your root password is. This will provide a graphical means to setup samba.
Part B of 2: If your using it in two places, one with DHCP and one without, then is each place using the same general ip subnet whatever, such as 192.168.16.* or 192.168.0.*
If they are using the same then assign your linux box a static ip manually within that ip range.
3. I dunno, as a general rule of thumb you buy what works with linux, though in your case you had this stuff already. You'll just have to keep asking people and google.
4. Yes you can with Windows Services for Unix.
http://www.microsoft.com/windows/sfu/
its a hefty download but this will allow you to setup an NFS share. Then when you bootup the slackware box you can type network and let it load the network module for your card. If it can't find one for you, then tough luck. You'll need to get it yourself and load it. Then when you start setup and it asks you installation source you can choose nfs share and go from there. Be aware though setting up windows services for unix isn't exactly noob friendly. You could also use NFS instead of samba after the initial install to share files as well.