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I save these to do on holiday hence the proliferation of queries.

5a. Venture firm corners South Africa (6) ???a?? Could it be safari but why?
13a. Stand-ups fall for Flook, for example. (5,5) ?o?i?, ??r?? Could be comic turns but don't understand Flook, dictionary says it is part of an anchor?
29a. Grow approximately 50 for the first time in grounds. (8) ?????a?e
31a. Innocent Eddy worried about English river (4-4) ?????, eyed
8d. A special radio broadcast engaging people overseas (8)????s?r?

13 Comic strip
https://en.wikipedia.org/wiki/Flook_(comic_strip)

5. ha za rd

31 dewy eyed

de wye yed

31 de wy e yed

8d diaspora
anagram : a sp radio

29 escalate