Hi Igor,
In question 1, the noun 'process' is followed by a qualifying phrase- 'photosynthesis'. SO we should include 'the' b4 'process' as a rule.
3) Since vaccine should be used by some one it should be in passive form .'was used is correct.
4)Since there are no Determiners before "important dicovery" it should be in plural form.
Nadiya