Thank you for your query.
You have two questions:
1: Driving Offence- you must apply for your extension visa before your leave expires otherwise you will become an overstayer. You have no choice but to apply. You will have to disclose your drink driving offence and the Home Office will take this into consideration when they make a decision to your case.
2: You may use your old English language certificate as confirmed in the Home Office guidance:
2.5. Applicants who already have a test certificate or result A partner or parent applying for leave to enter or leave to remain is not required to provide evidence of meeting the English language requirement if they have done so as part of a successful previous application as a partner or parent. Paragraph 32D of Appendix FM-SE provides for when this earlier test certificate or result can and cannot be used.
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