This is mainly for the Malays to answer as it is related to the culture. Recently I check on a lot of blogs about engagement rings and the men usually pick up rings with jewel for their engagement day. My question is, is is still appropriate to use a ring without a jewel (cincin belah rotan)?

yes

I gave my fiance two rings. One is belah rotan (for merisik). Another is with stones (for the actual engagement). But that's because for nikah I don't want to give another ring, but something else.

But I don't think it's wrong if you give belah rotan only for engagement. It's only adat, not as important in our religion.

Depends on your budget. But usually belah rotan for risik only

I gave cincin belah rotan to my wife during risik and engagement (same day ceremony) and another jeweled ring during nikah... I think that's enough