Where can I get a citizen card for immigrants?

First of all, your girlfriend should apply for a single certificate in Taiwan Province Province, and get married with you in the mainland with that certificate. You can apply for foreign-related marriage registration in the mainland (I used to go to the capital, but I don't know if it has improved now).

After getting the marriage certificate, bring your ID card, notarize the household registration at the local notary office, and send the notarized copy to the Immigration Department of Taiwan Province Province. The Immigration Department will issue an entry permit, and with this entry permit and marriage certificate, apply to the local entry-exit administration department for a mainland pass. You can use these two certificates to buy a plane ticket to Taiwan Province Province.

To get a Taiwanese identity card, you need to stay in Taiwan Province for 6 years continuously, and you need to stay in Taiwan Province every year for 6 years 183 days (half a year), which can be accumulated. The extra days are not counted, but if the number of days in a year is less than 183, you have to start over.

I remember that I can apply for a long-term residence permit after two years in Taiwan Province (from the date of entry), and then I can apply for an ID card after four years. When you apply for long-term residence, you need to apply for a citizen card, which means that you have no criminal record in the Mainland. If you do, I'm afraid you won't get your ID card.