Why is ''Grandmother misses her grandchild'' marked as incorrect? How are we to know if there's only 1 child or more the sentence is reffering to?
The possessive gives it away – sina is plural, so it must be several grandchildren. If it were about one child, it would be sitt barnbarn. (and if it were some common gender word, it would be sin, like sin hund 'her dog').
saknar is when you miss someone like in you wish they were there.
missar is when you miss the target or miss the bus
If Granny missar sina barnbarn, maybe she was shooting at them? :D
Is it correct to pull the "r" from mormor and the "s" from saknar together to pronounce it with an "sh" sound? The TTS seems to do so, but for me it's counter-intuitive.
Yes, it's correct. For speakers who pronounce the /r/ in the standard way, it will blend together with a following /s/, even over word borders. There's a lot of variation in how r is said in different dialects so it doesn't happen for all speakers. Also, r:s don't blend when they're dropped altogether and if we speak extra slowly and clearly it might not happen either. So it isn't super important to make the 'sh'-like sound here.
We only have the one word for it so it covers both, but grandchildren is the standard word in English so I'd usually go for that.