There are 2 airports in Osaka - Kansai & Itami. The most convenient way is travelling by taxi, however it is not cheap. I would suggest taking the airport limousine bus and the JR line. You can always use Google Maps to check on the schedule.

Kobe port is pretty big, so make sure you know where you are and where you're going. Walking or subway/trains is the easiest option. Buses in Japan is a complicated business!

I assume you are talking about Temamashi Station which is at Osaka. You need to get to Kobe via the trains because thats a different city...abt 20 mins away via shinkansen. You will arrive in Shin Kobe. Take the JR Train to Sannomiya Station. Then from there you can switch to the Kaigan line to Harbourland Station. If you wanna go to the Kobe Port Tower you have to stop at Minato-Motomachi station and go for a 5min walk towards the tower.

近くに沢山あったような気がします。料金が高めで、休日は渋滞がよくあるようなので電車、地下鉄が便利かと思います。

ＪＲ神戸駅の海側に市営の地下駐車場があります。買い物等の予定が無ければ、料金的には一番安いかと思います。 地下街（デュオ神戸）と連絡しており、ハーバーランドまで徒歩５分です。神戸駅南駐車場で検索してみて下さい。