iTunes and iPod Touch

"Please Note - I have typed up a long and complex answer to this question, however in short this is one of the few times I highly recommend you read the manual available here. To answer each one of these in detail will be the same as rewriting the User Manual. All of the references I have quoted in this answer is from there.

Applications from the App Store

iTunes automatically syncs applications you’ve downloaded or purchased on iPod touch to your iTunes library when you connect iPod touch to your computer. This lets you access the downloads on your computer and provides a backup if you delete applications from iPod touch.

You will need to download these apps again, as they are not linked to your iTunes account. If they had been purchased by the previous owner you will need to purchase them.

Step to update Firmware

This is done through iTunes. On the iTouch summary screen in iTunes is an update firmware button which will do everything automatically.
Thanks to Nagul, the iPod Touch firmware is charged for and available from Apple here.
As per the OP, if the iPod Touch is reset the update is free

Syncing Music, Videos and Podcasts

Set up iPod touch for manually managing content:
1 Connect iPod touch to your computer.
2 In iTunes, select iPod touch in the sidebar.
3 Click the Summary tab and select “Manually manage music and videos.”
4 Click Apply.

To reset the phone:

Reset all settings:

Choose General > Reset and tap Reset All Settings.
All your preferences and settings are reset. Information, such as your contacts and calendars, and media, such as your songs and videos, aren’t deleted.

Erase all content and settings:
Connect iPod touch to your computer or a power adapter.
Choose General > Reset and tap “Erase All Content and Settings.”
This feature resets all settings to their defaults and removes all your information and media on your iPod touch by overwriting the data stored on iPod touch.

For a lot of good tips on using iTunes to manage your iPod, iLounge has some very good tutorial available here"