Nope, the Surface has a tablet processor inside it. It's the same reason you can't install Firefox or Adobe onto an iPad or a cell phone.... the processor inside simply can't run that kind of program.
You can buy the Surface Pro instead of RT, and it has a full computer processor in it. However a full PC processor gets hot, so it's also thicker, heavier, and has a cooling fan to keep it from getting too hot. You'll notice iPads and Android tablets are thin and have no cooling fan, and they also can't run these programs you mention. It's all the same anywhere you go.
I actually have a Surface Pro and tried Google Chrome on it, but Google doesn't support touch screens very well, and it's very difficult to use (impossible on most websites). So you really are better on the Surface RT using Internet Explorer. It has features like Chrome that you might not know about: syncing your bookmarks and your tabs, passwords, etc.
As for Adobe: There are indeed official Adobe programs in the Windows Store.