I have a peanuts allergeny.

I have an allergy BUT peanuts are an allergen

For the first time in a while, I tried to eat cookies that contained crushed peanuts.

contain = present (if you are eating the cookies right now)
contained = past (if you ate the cookies earlier)

However, I could only eat one because I thought I'll bewould not be feeling well.

I have peanuts allergeny.

For the first time in a while, I tried to eat cookies that contained crushed peanuts.

However, I could only eat one because I thought I'll be nothat I wouldn't feeling well.

When I eat Kameda Crisps, I firstly separate the crackers and peanuts and eat only the crackers.

It was convenient because my father liked peanuts.

While this is a grammatically correct sentence. It doesn't really make sense contextually. If you're implying that your father has passed away, then you would use this sentence. However, if your father is still alive, you would say, "It's convenient because my father likes peanuts" or "It was convenient when I was a child because my father likes peanuts".

I have a peanuts allergeny.

For the first time in a while, I tried to eat cookies that contained crushed peanuts.

However, I could only eat one because I thought I'll be no might feeling unwell.

When I eat Kameda Crisps, I firstly separate the crackers and peanuts and eat only the crackers.

It wais convenient because my father likeds peanuts.