Are 无期 and 无限期 same?
无期 (without time limit) in '无期徒刑' is short for '无限期' . However, the term '无期徒刑' itself is a common set phrase for 'life sentence' . Therefore '无限期徒刑' is considered incorrect phrasing of "life-sentence' , although it is not grammatically incorrect. ('无限期' as an adjectival phrase that modifies the noun '徒刑')


无限期 (without time limit) is a phrase made up of 无 (without) and 限期 (time limit). 


When used as an adjective, it requires an adjective marker '的' as in '无限期的徒刑' (jail sentence that without a time limit)
When used as an adverb, it requires an adverb marker '地' - as in '无限期地監禁' (indefinitely imprison)
'无限期' can also be an adverbial phrase, and modifies a verb without marker, as in '无限期罢工'


无期 (never) in '會再无期'(no date/ never to meet again) is an adverb