The difference between citizenship and residency primarily lies in the level of legal status, rights, and privileges granted to an individual in a specific country. A Citizenship grants you all the the privileges while a Residency can restrict you from some.
Yes, you can include spouses, children, parents, grandparents and in some cases siblings. Family members are added if they are within the required age according to each country's requirements.
If you're applying to a direct Second Citizenship program the answer is no, you can obtain the passport without having to travel. However, if you're applying to a Residency program, you'll need to travel to submit your biometrics during the process and reside in the country based on the residency requirements of each country to obtain Citizenship.