Yes for past tense you will say думала if female and думал if male. This applies to other past tense forms as well such as читала, ждала, говорила, etc. The present tense doesn't discriminate between gender as both male and female would say "я думаю." It's very similar to French if you have any experience as it's equivalent to pensé/pensée for past and pense for present.
This is actually a fairly complex question you are asking.
In Russian, the verb is clearly present tense because that's how these sentences are constructed. However, in English we must switch to past tense ("red") because of English grammar rules (sequence of tense). This rule does not exist in Russian.
The Russian sentence could also be written in past tense by making the following changes:
1) Я думал, ты много читал(а): you could potentially use the same English translation here, but I would rather use something like "I thought you used to read a lot" or "I thought you had been reading a lot" to clarify the difference.
2) Я думал, ты много прочитал(а): again, this could use the same English translation, but for this I'd rather use something like "I thought you had read a lot" to clarify the difference.
Not being a native speaker, I may be missing the subtle implications of the various Russian verbs, but the fact that English has far more tenses than Russian definitely complicates the issue — as well as the Sequence Of Tense rule AND, of course, the fact that read and read are spelled the same.
Short answer: It's past tense. "Red".