The pop3 protocol (and that's what you're using) has no command to to specify the age of the messages you weant to download.
Maybe it's possible to do this with a selective download filter. Create a selective download filter, with the condition 'age is greater than 30 days' and the action 'ignore and mark as read'. As I understand these things, TB will download the headers of all messages in order to decide what messages match this condition and won't download them, but I've never used this feature myself, so my understanding may be faulty. As long as your v5 setup also says keep messages fo a year, new download sessisons won't take as much time as the first session when TB has to check all messages in your account.

That's because gmail is merely acting as a pop3 server. You can tel gmail that you don't want to download old messages, though you cannot download them twice with different computers or clients without changng the settings  (every time) between two downloads. With real pop3 servers you can download the messages as often as you like as long as you set 'keep messages on server'.