I think 80 years is the very upper limit for apple/crabapple trees. The wood is quite beautiful but it's hard to dry in large pieces without cracking... but the wood's fantastic for making replacement tool handles if you have a lathe. But I digress...
Go ahead and plant the seeds, but whatever comes up might be like the original tree, it might be a lot different. It really depends a lot on where the pollen came from.
Old crabs, like the Bechtel with its double white blossoms, are quite beautiful but aren't at all resistant to apple scab which defoliates the trees by August if you're in a place where the disease is prevalent. There are tons of newer varieties, some of which are quite resistant to scab and other diseases, available in lots of different colors and fruit sizes/colors. Do some research -- in my opinion some of these are kind of garish. There are crabapple test grounds scattered around the country -- Ah, here's a link --
http://www.malus.net/ , select "Evaluation Programs" from the frame at left. Check the site nearest you next spring to see what you like, ask for a recommendation or two.
And be aware that like many other members of the rose family you won't be able to plant a crabapple anywhere within the root zone of the old tree for a few years due to "Specific Replant Disease". The roots give off a poison that only affects the same species.
on edit: removed an error or two