What are Jewish conventions regarding honeymoons? Is a honeymoon taken, and, if so, is it done immediately after the wedding--or later, once the woman is again tehora?
There is no sanctioned "vacation" in Judaism or Jewish weddings. The whole concept appears to be a "new invention" even in Christian Society.
However, "honeymoon" periods do exist.
Firstly, there is the week of sheva brachot, where all meals are supposed to be joyous and glad with many members from the community. There is also a custom to invite people who could not make it to the wedding.
After the week of Sheva Brachot, there is also a concept known as "Shana Rishona" Or "The first year". During the first year of marriage, the couple, if possible should never spend a night apart. They should not invite guests for Shabbat, and A soldier should not go to war. Over the generations, other customs have grown out of "Shanna Rishona"
As for the aspect of being Tahor I have seen various customs on the issue, some of which arguably go against halacha.
One custom I have heard of is that after the first night of marriage, the couple does not consummate the marriage, so that they may touch each other during the week of Sheva brachot, and only once the stress has been reduced, and family is gone, and "life is normal" do they sleep together. As far as I am aware, this is a common custom, yet not approved by anybody.
Another custom is to have a 'honeymoon' on the evening of the wedding, where the bride and grooom will spend the evening in a fancy hotel, and they will spend the first day together before getting involved with the family and friends for the sheva brachot.
Another custom I have seen, is to take a "honeymoon" months after the wedding, waiting for a good time in the calendar where they can have a long weekend together and go away.
The modern custom of honeymoons raises a significant halachic question, famously addressed by R. Yitzchak Abadi in his sefer Ohr Yitzchak which is the problem of "dam besulim". After the first time a couple is intimate on the wedding night, they are normally required to avoid relations until the wife becomes pure again, as you allude to in your question. But on honeymoons, which most couples take immediately after the wedding, couples are generally assumed to have relations again, within the prohibited timeframe. R. Abadi attempts to find a way around this problem in order to make sure that the majority of couples that go on honeymoons are not transgressing. His approach is rejected by R. Shlomo Zalman Auerbach, whose response is published in R. Abadi's sefer along with R. Abadi's rebuttal.
Saw three opinions re: taking a honeymoon immediately after a wedding cited in this OU article about Sheva Berachot:
1) Rabbi Ovadiah Yosef
Even though making daily sheva berachot is not obligatory, halachah does not endorse the secular custom of a honeymoon either. Rabbi Ovadiah Yosef (Yabia Omer 3:EH:11:11) strenuously objects to such a practice and views it as indicative that the couple “is not interested in the berachot.”
2) Rabbi Aryeh Kaplan
On the topic of the honeymoon, Rabbi Aryeh Kaplan (Made in Heaven: A Jewish Wedding Guide [New York, 1983]) writes:
It is not the Jewish practice for the bride and groom to “escape” on a honeymoon right after the wedding. Rather, they remain in their home community. They are beginning their married life, not separated from the community but as an integral part of it (p. 230).
3) Rabbi Shlomo Aviner
Rabbi Shlomo Aviner ("Rayim Ahuvim" pp. 167-169) is in the minority when he says he sees no problem with a honeymoon and that couples should do as they please.
AGAIN, IMPORTANT TO NOTE:
Even those cited above who are opposed to honeymoons (R' Ovadia, R' Aryeh Kaplan), they seem to be only referring to a honeymoon IMMEDIATELY after the wedding.
A honeymoon taken a few weeks/ months after the wedding would seem to be fine to everyone as it's nothing more than a nice trip for the husband and wife!