This thread will now be used not just for the wheel truing, but to ask any other questions related to the same bike as I work on it to learn wrenching, and hopefully improve the bike! I don't want to create a new thread each time. I can't update the title of the thread to reflect this though.
I took it for a short ride - seems to have held up. Need a longer ride though, which will be challenging since the bike isn't my size - its too small. It was bought just for my wife to figure out if she can still bike

We will probably get her a new bike now, so this one is mine to mess around with.
The brakes seem to have improved a lot. I had ridden it before, but the stopping power of the brakes seemed so much better now.
Next: change the rear shifter - the current one is broken. I'd like to change the rear cassette/freewheel too (not sure what it is at the moment) - so I'm going to be looking at ebay lots I think. 7 speed parts are really hard to find though, how do I figure out whether I can move the bike up to an 8 speed in the rear?