Is it permissible to say: "I seek forgiveness from Allah for every sin I have committed... and I repent to Him"?

Seeking forgiveness (Istighfar) is a great act of worship. The Shari'ah has not specified a particular number for it. The fact that the Prophet used to seek forgiveness seventy or a hundred times does not mean that this number is restrictive or preferred; rather, the command is general to do it frequently. The formulas mentioned in the question are permissible, but it is better to stick to the formulas narrated from the Prophet, may Allah's prayers and peace be upon him.