Hi Ohso, DNS propagation can take upto 24 - 72 hours. It depends on Registries. However, not all registries make quick updates of their zones basically. To protect their root nameservers from overuse, they set High TTL value. If you are lucky around 4 - 6 hours it is going to take. Ping your...
1. Yes you can add your own domain name on free plan, they allow up to 2 Addon Domains on free plan.
2. For moving the forum follow the steps :) -
a. Download all the files in the SMF forums backup
b. Backup your SQL database.
c. Setup a new database on your new host.