Many thanks for your letter - it was really nice to hear from you again.
In connection with : this is a little formal for a letter to a friend. What about:
To answer your questions, I'll try
to give you some more details : have you already written giving some details about getting to your home? It doesn't sound like it from the letter your 'friend' sent to you. So:
to explain how to get to my home from the airport. There are three possibilities. Firstly, you could take a taxi, but I have to warn you about taxi drivers: they could ask you to pay more than it really costs. Secondly, you could take the bus, but our buses aren't so comfortable. Lastly, and I recommend this one to you, is my car.
I'd like to wait for you at the airport. : I bet you wouldn't, especially if it was an hour late! lol. I think you mean you would be happy to meet her at/pick her up from the airport.
I'll be happy to meet you at the airport, and best of all, it won’t cost you anything!
Now, the second issue of your letter was the weather. : This again is a little formal. You might say:
You also asked about the weather.
I've checked the weather forecast for March and we may
also : if you had written, it will be mainly sunny, but we may also have... 'also' means, 'as well as', but there is no mention of anything before the 'also' that you are adding to.
have some cold and rainy days. If I were you, I'd pack a thick sweater. A raincoat is also recommended.
I’ll finish now as I’m running out of space. I look forward to your arrival/to seeing you.
All the best,
Student or Learner