Is it permissible for a Muslim to exercise ijtihad (independent reasoning) in some jurisprudential matters, such as not performing ablution for the third time when flatulence is emitted from the anterior private part for the second consecutive time due to hardship, and will he be held accountable for that for not having asked?

Ijtihad (independent reasoning) is for well-grounded scholars, and the layperson should ask them, as Allah Almighty says: "So ask the people of the message if you do not know." The one afflicted with Waswas (whispers/obsessive thoughts) should disregard them. If the emission of gas from the front passage is merely a doubt, then do not pay attention to it unless you have certain conviction that you can swear upon. Disregarding Waswas is what Allah has legislated for you. However, if you are certain, with absolute conviction, about the emission of gas from the front passage, then ablution (Wudu') becomes obligatory. You are permitted to follow the madhhab (school of thought) that does not necessitate Wudu' for gas from the front passage, in order to repel Waswas.