Did Gao Zhan bed Shen Bi and end up having a baby with her?
Nope. (Can I scream hell yay!?) According to the novel, the whole thing was mastered by Empress Dowager Lou. In the trailer, it shows Gao Zhan drugged and he mistakenly sees Shen Bi as Lu Zhen. Contrary to what is implicated in the teaser trailer, supposedly nothing happens between Gao Zhan and Shen Bi. No sex. No pregnancy.
Did Gao Zhan and Lu Zhen actually get married?
Yes, the wedding scene we often saw in photos actually took place in the story. Gao Zhan and Lu Zhen married in a quiet ceremony because his sister just got killed in the rebellion.
Why couldn't Gao Zhan make give any formal imperial titles to Lu Zhen?
In order to quench the rebel forces, Gao Zhan solicits the help of a ruler from another kingdom. This ruler at first agrees to help Gao Zhan anti-rebel effort and Gao Zhan's wish to make Lu Zhen his future empress. He later rescinds on his decision and forces Gao Zhan to entitle his favorite daughter, Princess Tonghua, as Empress of Northern Qi. To save Northern Qi and save Gao Zhan's health (currently suffering from some type of poison), Lu Zhen leaves Gao Zhan for three years.
How does Lu Zhen become prime minister?
Because Lu Zhen couldn't become his empress, Gao Zhan appoints Lu Zhen as his prime minister. She would rather work besides him as a political minister than become a frivolous court lady.
Does Lu Zhen become infertile?
Yes. During the rebellion, Lu Zhen jumps off a high fortress to prevent Gao Zhan's enemies from using her to make him surrender his forces. The fall causes Lu Zhen to slip into a deep coma. The medication that the royal physicians used to revive her destroys her chance of ever experiencing motherhood.
What happened to Shen Bi at the end?
She dies from saving Gao Zhan in the rebellion.
What is the ending for Legend of Lu Zhen?
Gao Yan dies from an arrow. Xiao Huanyun dies in child labor shortly after Gao Yan's death. Gao Zhan ends up dying from his old injuries after becoming emperor. Gao Yan and Xiao Huanyun's son succeeds Gao Zhan as the next emperor. Lu Zhen survives everyone and counsels Gao Zhan's successor as prime minister. Fifteen years after Gao Zhan's death, Lu Zhen's tumultuous life also concludes. She once again breaks tradition by being buried in next to the late Emperor Xiao Zhao, Gao Zhan.
The above spoilers are based on the novel. The actual drama may make some minor or even substantial changes.