Here are the corrections for the underlined parts of the sentences:

1. I'm putting aside some money because I want to buy a new car in two years. (We use "in" to refer to a point in the future.)

2. Linda and Alice will be on television this evening to talk about future communication. (We say someone is "on television" or "on the radio".)

3. Jim liked his Christmas present sent by his granddad, but his little sister, Jully, didn't like hers. (The conjunction "but" is used to show contrast.)

4. Daisy enjoys going shopping, playing sports, and hanging out with friends in her free time. (To maintain parallel structure, all items in the list should have the same grammatical form - in this case, gerunds.)

5. Teenagers are greatly influenced by not only their parents but also their peers. (The adverb "greatly" correctly modifies the verb "influenced".)

6. We have never been to London, so I wish we could have a chance to visit this capital city one day. (After "wish" when talking about a desire for something possible in the future, we use "could".)

1. I'm putting aside some money because I want to buy a new car in two years.
2. Linda and Alice will be on television this evening to talk about future communication.
3. Jim liked his Christmas present sent by his granddad, and his little sister, Julie, didn't like hers.
4. Daisy enjoys going shopping, playing sports, and hanging out with friends in her free time.
5. Teenagers are greatly influenced by not only their parents but also their peers.
6. We have never been to London, so I wish we could have a chance to visit this capital city one day.

1. I'm putting aside some money because I want to buy a new car in two years.
2. Linda and Alice will be on television this evening to talk about future communication.
3. Jim liked his Christmas present sent by his granddad, but his little sister, Jully, didn't like hers.
4. Daisy enjoys going shopping, playing sports, and hanging out with friends in her free time.
5. Teenagers are greatly influenced by not only their parents but also their peers.
6. We have never been to London, so I wish we could have a chance to visit this capital city one day.