Narjiz

Couldn’t tell since it was not written in letters I could understand 

As a pharmacist, I'll tell you it can be done and I have done it. It is legal, however, in the first months there were no clear rules on it. With the increasing numbers of fake vaccine records, there is probably a lot of hesitancy. The new system has a place to enter the lot number of the vaccine. It unfortunately only recognises ones given in Germany. Entering the lot is optional, but we all enter it to be safe. This may be another reason why the pharmacy did not want to do it. here is no pflicht on the pharmacy side, so theoretically anyone can outright reject you and and do not need to give a reason.    As long as you bring your original proof of vaccination with you and your ID (passport) we do process them. Each person needs to personally show up (including kids). No bringing passports and vaccination records for the entire family yourself! The CDC card is accepted as far as I'm aware. The only one I outright rejected was from a Chinese couple with a vaccine record completely in Mandarin. It has to at least be in letters I can decipher and look legitimate. Maybe try getting it done in a bigger city where pharmacies are used to seeing a more international crowd. 

You won't find an answer. The answer is it depends on who is processing your file. From those I personally know, it did not impact their file, but that is only what I know... 

I know people who did not do it but I think the requirements changed after and now everyone needs either leben in deutschland or the Einbürgerungstest. I signed up for the second because the leben in DL test is not open to those who did not do the integration course according to the several VHS and the ABH I contacted. Just download the app and do 20 questions a day and when you get them wrong memorize the answer and go on. You need German for sure. I remember reading the questions a couple years ago when I was in my B1 course and I struggled to understand a lot of the questions. Reading them now they are pretty easy questions but you do need to go through them. 

Third country national here. I always present my Aufenthaltstitel first (give them a couple of seconds to actually look at the card), then I hand over my passport. To this day I have never had my passport stamped.     

Yes, of course you can travel. 

Sorry I can't say. I can only tell you our experience which I already explained. The timing of appointments has been changing constantly so I don't know what is going on. 

I am actually wondering how they decide to add that? My residency permit is for 3 years and says my passport number. Most people I know in the next Gemeinde over (less busy one) have passersatz on theirs. Just curious honestly. 

Yes you have to give your passport when you get your urkunde. A passport application does not take long, I believe it was about 4 weeks after application.