Cambridge English: First

'Hi' is the correct spelling.

This should be 'having'. We always say 'look forward to +ing something or somebody'.

Try saying something like this: 'You asked about how to get from the airport to our apartment - well, don't worry, it won't be difficult'.

The verb 'call' does not take 'to' so this should be 'call the airport'

This should be 'arrival time'. 'Estimated time of arrival' is an alternative but is also rather too formal.

This sounds a little TOO informal! How about 'Does that sound alright to you?'

This should be 'As for the weather....'

This should be 'Swedish'

You need something to indicate a pause here such as a semi-colon or even a full stop.

This would be better as 'bring''

This should be 'warm clothes with you''

Try something like 'And finally, let me add something about the issue of money.'

This should be 'try not to think about it.'

This should be 'I am looking forward to seeing you.'

Don't forget to sign off your letter, with 'Love from' or 'Best wishes' followed by your name.