So the sentence "I'm looking for someone to talking with" it doesn't take the same way of "I'm looking forward to seeing you" ? the correct answer " I'm looking for someone to talk with"

Hello, I am an American so my grammar can sometimes be off. But as far as it sounds to my ear, "to" almost always takes infinitive after. "I wanted to talk with you" The only time I can think of when to takes gerund after it is when you say " I am not opposed to talking with my grandma. "opposed to" is the phrase which takes a gerund after it. but 99 percent of the time, infinitive is the way to go.

Maybe "to talk and to improve" will be a better one. For the most normal time, we will choose "to do" instead of "to doing" except the special sentence structure and sometimes we'd love to use " to doing" to emphasize the action.