[Hampshire] Local mail

I've a couple of queries about local mail on Linux (the mail that things
like cron jobs send) that I'm hoping someone can point me in the right
direction on.

The first is: is it possible for Thunderbird to read local mail as my
googling so far indicates not. It would be very useful, as at the moment
I have to remember to run mail, whereas I run Thunderbird out of habit.

The second is: is it possible to get my server on my home network to
send its local mail to my desktop. Again, so I don't have to remember to
check it?

Thanks,
Leo