The bus that connects Tarragona to Zaragoza is run by HIFE. The bus that goes from Zaragoza to Huesca is run by ALOSA although I think it has been bought recently by another company it might be still operated by that name. Check the websites. There are many services between Zaragoza and Huesca, every hour at least. I am not so sure between Tarragona and Barcelona.
If you go by train it might be much faster, because it is an AVE, High speed train but all depends on the time you spent in connections. I am not sure where the AVE station is but it is between Reus and Tarragona, so it might easier to go to the train station than to go the bus station. It will be more expensive by train. So you can go to Zaragoza by train and then by bus or train to Huesca. There is no direct connection between Tarragona and Huesca by train or at least not many. Because between Zaragoza and Huesca you have to change, it might be worthy to go by bus, it would be cheaper, more frequencies and probably only 10 or 15 minutes slower.
Thanks,mgilgar, for all your suggestions. Now we can do some serious planning.
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