You can either say “I prefer going to the park.” or “I’d prefer to go to the park.” “I prefer to go to the park” sounds unnatural to me.

If you use the gerund, you’re usually referring to a habit. I like going to the beach but I prefer going to the park. If you say ‘I prefer to go the park’ it can sound more like a one-off action (though not always). Would you like to go to beach now? Hmmm tbh I prefer to go to the park.

"I also love" sounds much more natural than "I love also." You can use either the gerund or the infinitive after "prefer."

*in the second one I don’t understand if it is mandatory the continuous form, or the infinitive form or if both are correct