We should consider several schools of thought on this. Firstly, insects do not behave in a way that suggests any kind of emotional life resembling that of humans. They have tiny simple brains and consequently a lot of their behaviour is produced by simple reflex responses to stimuli. Also, regarding the second question, this assumes that a mosquito would recognise its brother, which is doubtful, their eyesight is pretty poor and their brains unsophisticated. There is plenty of evidence that many insects have little or no sense of family bond, in fact sometimes their behaviour is much worse. Female praying mantis cannibalise their mate during mating. The orange tip butterfly usually lays just one egg per plant, but if she lays two one of the emerging caterpillars will probably eat the other, sibling or not. Social insects on the other hand do cooperate with other family members, eg bees. They will also exhibit high levels of self sacrifice in the interest of their colony. However, there is no evidence that this behaviour is regulated through emotions.
Secondly, Charles Darwin famously suggested that animal emotions include love, jealousy, anger and terror. Studies have shown that bees become more optimistic than other bees when rewarded for reaching certain sites. Does this demonstrate that insects have the cognitive and physiological building blocks that might give rise to complex phenomena such as emotion?
Lastly, wasps are another social insect. If you have been unfortunate to disturb a nest you will know that they can certainly display anger, a pheromone response triggered probably by fear. They also produce offspring and are social with their own species, though this is more a mechanical precondition, than something triggered by arousal or a need for company.
In conclusion then, perhaps insects display base emotions but whether they feel love, grief, empathy, sympathy or sadness is unlikely. As humans we can feel and demonstrate kindness to an insect, it remains unknown if these emotions are ever reciprocated.