What is the daily Pradosha kalam? It is said that one must not do japam, parayanam, recite Sri Vishnu Sahasranam, et al during prodasha kalam. How then can we do Ashtakshara mantra japam during Sandhyavandanam and do Srivishnu Sahasranam parayanam in the evenings?

All these must not be done during Mahapradosha kalam. It is also said that learning of Vedas is not allowed during daily pradosha kalam. It is a period to perform Sandhyavandanam along with Ashtakshara japam.
They might have laid down this stricture to ensure that nothing other than Sandhyavandanam must be done during this period. For example, some might be inclined to do Sandhyavandanam after reciting Sri Vishnu Sahasranam in the evening. It might have been said to ensure that it is not done so.