Re: subject verb agreement
The rule you've learnt is wrong or at least only partial. Living and studying is counted as the one activity when it is the combination of the two that made it difficult. Living there might have been easy. Studying there might have been easy. But living and studying there might have been difficult. (That's a bad example because studying in a country implies living there - or maybe that's what makes it one activity)
Originally Posted by arzgol
A more illustrative sentence might be, "Learning French and German together is difficult." It's more apparent here that 'are' is wrong.
In the second example, there is only one good idea - increasing lab hours and hiring new staff. Again, either factor by itself might not be a good idea. The good idea is doing both.