If I'm in a probationary period of work, can my employer terminate me if in need gallbladder surgery for stones and have to be off work for 14 days?

Generally, if an employee needs to miss work for any reason, including medical care, he or she could be fired unless:

1) he or she has and is properly using sick leave or other PTO he or she earned;

2) he or she qualifies for FMLA leave (or leave under a similar state law) and the employer is also covered (i.e. large enough; under FMLA, that means at least 50 employees); or

3) the employer specifically gave him or her permission in advance to take leave.

If you're in a probationary period, you probably do not have enough sick leave or PTO, and you would not seem to qualify for  leave under FMLA (or a similar state law), which typically require a year of employment. Therefore, it is most likely the case that you could be terminated for missing two weeks of work without employer permission.