no
You use the same thing as the ps3 and psp
Move them to a USB flash drive and use that to move them to the PS3 if the files are compatible with the PS3
the ps3 store i use it directly on my ps3, i am not sure if you can use it online though The PS3 PlayStation store is available only for the PS3 consoles that have online capability and it is the preferred way to download to your PS3. If your PS3 does not have an internet connection your PS3 can not access or use the PlayStation store . I know procedures exist to allow update information to be downloaded from a computer and moved to the PS3. The best source for procedures is the PlayStation network support at related link
No they are 2 separate things.
You can't use a PC, you either transfer certain titles from a PS3, or get them directly from the PSN.
The PS3 must be connected to a TV and some PC have TV capability but will not make the PS3 have any computer function during gameplay
If the hotel has broadband WiFi you don't need the computer just use the PS3 WiFi connection and if it has Ethernet then plug the Ethernet cable in your PS3.
You only need a PSN account not a new one
no
Nothing. You can not use the computer in the game to be 15 prestige
Technically yes you can. Your PSN account is a Sony-wide service regardless of the device you are using it on. You can redeem a PS3 code while on the PSVita's own PSN 'app', and it will be added to your PSN account. However of course, that will not let you use the PS3 content on the PSVita.
To transfer music on your PS3 to your iPad 3 you can simply back it up from your PS3 to your computer and then use iTunes to put it on your iPad.