I have this tree in the far corner of my lot and I was wondering what kind it is. Does it flower or produce fruit?
Yes, the purple-leaf hazel produces nuts: a little smaller than other hazels, but good. It will produce some on it's own, but you'll get more if you've got two, or there's another hazel in the neighbourhood. The leaves will turn green later in the summer, which is normal. They'll come out purple again next Spring.
That's good news. I wonder when they produce nuts, in the fall? I don't think there is another one in the neighbourhood but why would having another tree close by mean more nuts?
Because the flowers mature at seperate times and so self-pollination is not sufficient to produce a good crop. It will produce nuts but not as much as it would if there was a way to cross-pollinate with another specimen.
Likely to be Purple-leaf Filbert Corylus maxima 'Purpurea' (the common purple-leaf plant in the genus).