It is one fo those particular cases where you can use both... It depends on your point of view. Btw, in everyone of the combinations, the idea is the same. Estuve muy ocupado en el trabajo porque tuve que leer montones de emails. Both actions (estuve/tenía) really happened (with a beginning and an end). Estuve muy ocupado en el trabajo porque tenía que leer montones de emails. The first action (estuve) happened, and the second one we don't know if it had an end. Estaba muy ocupado en el trabajo porque tuve que leer montones de emails. Here, "estaba" shows the action as an entire event, I mean, your point fo view is located as a spectator while the event takes place. And, "tuve" shows a punctual action, with a end, in the first event. Estaba muy ocupado en el trabajo porque tenía que leer montones de emails. In this last one, "estaba" works like in the last example, and "tenía" like in the second one. It's the description case. It doesn't work always. But, in this case it does. Of course, a native person uses it with naturality without thinking in all these above. You can use whatever you want to, but here you have the difference. I hope this helps. If you have questions, feel free to ask. Saludos.

It depends on what you mean -- on your point of view. Probably, tenía, because you are referring to a past ongoing situation, not a concluded action. (Even though it may have subsequently finished, that is not the point of your statement in context.)

Puedes usar los dos no hy ningun problema pero el mas apropiado es "tenia"

It's actually a description of what you were doing so you have to use: " tenía "

puedes usar ambos, significan lo mismo //You can use both, mean the same