1. By taking a vaccine, are we in moral cooperation with murdering babies?
No. You can be against abortions and still take the vaccine (and modern medicine). I think this question should be expanded to include modern medicine, not limited to vaccines. Someone who is against vaccines would also be against modern treatments as they are very likely to include involvement with fetal cells (such as monoclonal antibodies). Do you think if someone takes living-saving Aspirin, they are in agreement with abortions?
2. By taking a vaccine, are we demonstrating a material connection to evil?
Yes, but one can disagree with the evil. A lot of what we do are ultimately connected to things that go against the Bible. For instance, if you work for an LGBT-friendly organization (which most major corporations/government employers/MILITARY are, as most now celebrate Pride Day for example), does that mean you are LGBT friendly also? Is it possible to be part of an organization but still disagree with it?
3. Though we may not have been the ones to murder the babies to harvest their stem cells, does purchasing vaccine products validate and enable evil?
No. The fetuses were not aborted for purposes of creating the vaccines (and other modern medicine). Do you think if a church uses "bad" money donated to them to spread the Gospel (to clarify, the church wasn't involved the evil activity, but money donated to them is linked to "bad" stuff), they are validating evil? Similarly, with vaccines, something bad could be used for good.
4. Is taking a vaccine being in agreement with murdering babies?
This question is same/similar to question 1. No, you can still be against current and future abortions and still take the vaccine (and other modern medicine).
5. Is there a moral alternative to the vaccine?
The moral alternative would be take a treatment that does not involve fetal cells AND is effective. However, if such a treatment is not available (either medically available, or blocked by the government, or virtually impossible to access), then I believe taking the vaccine is fine as it is life-saving. Even though I believe the efficacy of the vaccine is not great (especially with Delta variant), I still believe it is life-saving either through direct or indirect contact.
If yes, then should the vaccine still be an option?
6. If taking a vaccine is a sin, (many Christians think it is) will it create scandal within the church for church members to take it?
Yes, there will be a scandal if one part thinks something is a major sin, and another part doesn't.