How to pronounce "s" at end of word when next word starts with "s"

Has and is are pronounced with a terminal /z/ when they stand alone. In your example sentences, the /z/ disappears and there is only one /s/ sound joining both words.

There is no need for an unnecessary s. Some people tend to hold the s on the first word into the last:

He issingle.

Not said quickly, the s is simply held. Others will enunciate clearly, making sure to pause in between the two words for clarity. Personally, I think it is better to enunciate clearly, as you will be better understood by those not familiar with English.

There is no change in pronunciation when the next word starts with an "s". There is no additional "s" sound". For your two examples, just say:

She has some apples. He is single.