Is the base game included with the Frozen Throne

Usually no,its a long shot but you could try this if you want to be sure. Depending on what are you trying to load you can try loading the game and finishing it then there might be option to save a replay automatically.

(if you played multiplayer,the replay after the point where it was saved will be retarded since you will be the only one left to finish it,but you can use the rest as video material)

If you have version greater than 1.24e in your options menu>gameplay you can turn on automatic save replay,and after finishing the loaded game you can check replays if it worked check in your warcraft 3 directory in replays folder,there it could be saved as "lastsavedreplay" and not recognized by w3.

Here you can set your hero skills to custom keys,it also has the option to set the inventory to custom keys(under "Extensions (Win Only)" tab).

Note that setting the inventory keys will require you to download additional script...the site has the guide for that so try it out.

This is your second option,I didn't tried it so i cant tell you much.