Chunk. There are ferries from Alcudia that go to Barcelona and to Menorca. There is a fast ferry that takes three hours to Barcelona and the ferry to Menorca takes two. Not sure of prices but you might want to look at http://www.balearia.net. It should be possible to book when you are in Alcudia either at the port or through travel agencies, though the fast ferry is often busy as the slow one takes eight hours.

You also asked about a jacket in June. It would be highly unlikely you would need one. If you were to get one, then make it light. You shouldn't need anything more.

You can fly Palma to Barcelona fairly cheaply if you book well in advance. Try the Air Berlin website they have a daily flight.
http://www.airberlin.com/site/start.php?LANG=eng&all=1
In June it is usually very hot, a jacket will be a waste of luggage space better taken up by light clothing. Take a very light rain protector just in case.