The detective was able to work out who it might based on evidence or reasoning so 'infer' is correct.

She is conveying a meaning indirectly (rather than saying it directly), so it's 'implied'.

The students could infer (deduce) that it will be challenging, but the teacher is implying (indicating/suggesting) it.

It's 'infer' as it's a conclusion based on evidence they see and reasoning (i.e. dark clouds and thunder usually mean rain).

The scientists are making a deduction based on the evidence they have so it's 'infer'.

His behaviour is suggesting or indicating to others that he is hiding something, so it's 'implied'.

The person is making a deduction based on evidence from what was said. So it's 'inferred'.

They are deducing this is the case from the evidence they see, so it's 'inferred'.

It's not being directly said that he disagrees, rather it is suggested by his tone of voice, so it's 'implied'.

'Seemed to' tells you that it's not being said directly. Rather it is being suggested or indicated. So it's 'imply'.