well you cannot choose your ship.
If thats where your relatives are living and you go there, you an get a day pass for them to onboard and see you...but like i said, USA ports are embaraktion day...so you will have no time hardly, only maybe an hour or so to make a quick call.
You do not get chance to stay on land for one night no...this is because the ship stays in ports for one day at the most, arrives in the morning and leaves at night...so you cannot be off the ship over night or you would miss it.
If you are doing this job you have to be prepared phisically and mentally to leave behind your loved ones for up to 8 months.
If you feel you cannot do this, then dont apply or you will be miserable. It is a very demanding life and you will not have time to be sad and miserable. They need positive people!...or they will send you home, really. Think about this before you apply, for your own good .
In answer to the internet question...yes we have internet onboard
We have a crew cafe, but its very slow as it is run by satellite. Also in ports there is internet cafes for crew that is very cheap that i use.
Hopefully i helped