I think it is important to clear something up here before going into the questions. /root is the home directory of the root user, not the root filesystem (that is a bit confusing, I know). The root filesystem is where all of the system directories go, and could roughly be equated to the Windows "C:\" drive. When making the partitions, you want to assign them to "/", which stands for the root filesystem, not "/root".
Now, to answer your questions:
1. The rule of RAM x 2 = swap comes from the days where machines only had a few MB of main RAM. On a machine with 2 GB of RAM, it is almost inconceivable that you will even access the swap space under normal use. Still, it is generally a good idea to have some swap available. I would make a swap partition of no larger than 512 MB on a machine like yours.
2. You can certainly get away with just one large partition and a swap partition. It isn't the best idea in terms of flexibility and error recovery, however. Having a separate /home partition allows you to use the same home directory between multiple installs of the OS. So if you needed to reinstall Ubuntu, or wanted to try a different distribution, you could do that without losing your files and user-specific configuration if you have a separate /home. It is really up to you, functionally there is no difference.
3. If this is just an experimental install, and not for full time use, you don't really need a lot of space for /home. It isn't like you will be storing years worth of documents and media on it. At the same time, you want to make sure you have a lot of space for / so you can install all the software you want to get comfortable with what is available. I would go for something like 15 GB for / and 10 GB for /home, or even 20/5.