1
I’m not a fan of cook, but I have to do it.
I’m not a fan of cooking, but I have to do it.
After a preposition such as of, use the -ing form of a verb: ‘a fan of cooking’, ‘afraid of falling’.
2
Speak English is difficult.
Speaking English is difficult.
When an activity is what the sentence is about, we normally use the -ing form: ‘Speaking English is difficult.’ ‘Swimming is fun.’
3
I living in Barcelona.
I’m living in Barcelona.
I’m live in Barcelona.
I live in Barcelona.
To form the present continuous, use am/is/are + -ing: ‘I’m living in Barcelona.’ In the present simple, do not add am/is/are: ‘I live in Barcelona.’
4
We went to the bar to drank a beer.
We went to the bar to drink a beer.
I tried to spoke, but I couldn’t.
I tried to speak, but I couldn’t.
After to in a to-infinitive, use the base form of the verb, not the past form: ‘to drink’, ‘to speak’.
See TO INFINITIVE