Hoping to hold/carry/lift baby easily for at least until 2.5 years, or longer. what do i need - upper body strength with weights? or core? or both? safe to do while pregnant too if up to it?

If you do not have any significant musculoskeletal disease, those are not big tasks. Keep yourself healthy with 3 hours of exercise with mild to moderate in intensity or 1.5 hours of intense exercise on a weekly basis, you should be fine even during pregnancy.

Good question. Mother nature generally has taken care of mothers for millions of years in doing this. Unless you have a specific problem should be no worry and no need to do weights etc. Discuss with your Dr who will know you better.