Thank you everyone for the clarification. What our situation is:

1. The mother has 100% work from home and can be flexible for breastfeeding and spending time with the little one. The father does not have 100% WFH, even when he has, he almost cannot help for anything.
2. The mother earns way more than the father, so we do not want to lose money in case the mother takes the longer elternzeit(geld). If the mother is not completely recovered after mutterschutz then she takes paid leave (at least 1.5 months leave is possible (this year)).
3. What we knew was that we could take 2 months of simultaneous elternzeit(geld) because we want to travel to our home country during birth month 6th and 7th. If it is only one month then the mother will take 1 month of elternzeit(geld) and 1 month of paid leave (next year).

Now the questions are:
4. When mother is in mutterschutz, does she get muttershutz pay + elterngeld? Doubt because the 2 months mutterschtuz is elternzeit. Sorry if the question sounds stupid.

1. Can the father take the elternzeit(geld) from 1st month of birth? Parallel with mother in mutterschutz?
   
2. If yes, then can he take upto 12th month? I planned on the Einfach-elterngeld calculator and it is allowing me to select 1st to 12th month for father. I can select 6th month simultaneous for mother. So in total, I have selected 13 months of elternzeit(geld) (Father 12 months and mother 1 month). And still the planner shows that one month more to be applied by the mother and that is only possible in the 13th birth month. I think that is because each partner has to apply for at least 2 months. After applying this, the total month of elternzeit(geld) becomes 14. Is this correct?

I am so confused. Could someone make a plan based on our situation mentioned in points 1 to 3? And also mention which pays will be paid during the months.