He is here on a 'work visa' yet he is working as a security guard when he is a microbiologist???
He would not get a visa to work as a security guard , work visas are only granted for highly skilled specialist jobs where there is a shortage of suitable people in the UK.
He does not want to go out to work ? of course he does not want to go out to work as he can't he is illegal . I bet the security guard job was illegal as well.
This all adds up, the dating site, moving in with your sister, giving up his job,telling your sister she can't go out with her own baby, he is here illegally and is using you sister to stay out of sight of the authorities .
Report him using woofgangs link.
I would not let him look after the baby , what happens if the child is ill or needs a doctor? Is he going to to take the baby to hospital or the surgery and risk being asked about his immigration status?