I wouldn't get an SSD in place of a HDD. You would be spending hundreds of dollars more to match that 1TB space. Also some SSDs usually don't last as long as a HDD.
There's no point, just because the case is bigger it doesn't mean that there will be any benefit in terms of airflow, or if it is even needed.
My above build gives you plenty of cooling, and a separate HDD and SSSD.
An SSD will give next to no benefit to stuff apart from OS and software, and will give a significantly faster dedicated speed compared to a hybrid drive, hence why SSHDs aren't recommended.
No, 240GB is what I would call a must have, 120GB can only store the OS, even then it can barely fit.
It is a very poor value investment.
Trust me, just go with this. PCPartPicker part list / Price breakdown by merchant
The build i have mentioned has everything optimized at the cheapest you can get. The SSD is more or less essential these days for faster load times and overall functioning of your pc. And the processors mentioned in these builds are locked and comes with stock coolers which are plenty to keep them cool.
Looks good, but you can spend less on the PSU given the low voltage draw of the system.
The 6GB 1060 will also perform much better, especially with a desktop cooler over an ITX variant. PCPartPicker part list / Price breakdown by merchant