I just bought the Monsters of the Multiverse but when I creating the character, there is no Farie or other race that come with it to be pick and no source option from Monsters of the Multiverse. Is it normal or am I getting a bug?  

Check if your entitlements are in sync.

https://www.dndbeyond.com/account/licenses

You should hopefully see the following.

Account Entitlements

Did you purchase from the site or through the app? Are you using the character builder on the site or the app?

Sorry for the late reply, I purchased on both platforms since I bought on the site and it couldn't work as it should be and now, I contacted the support for refunding the site's purchase. Hope they would refund my request soon.

My account is already in sync but it didn't work out as it should be, so I bought in the application for it to work out. However, I requested for refund for onsite purchase already but they didn't read it yet or maybe I got ignored somehow. 

Purchases can take a while to push, and the app doesn’t sync in real time, only once overnight I believe.

Support ticket times run approximately 3 weeks on average, and with the current state of things I expect even longer now. Be patient.