I have some questions regarding Ghadeer Khum and the whole incident with Khalid bin Walid and the slave girl and hating Imam Ali.

1. How many times was Imam Ali sent to yemen?

2. What year each expedition took place? the first and second.

3. The reason why imam ali was sent on each one and what occur each time if you can briefly explain.

I have heard that the incident of the whole "khalid and Imam Ali had conflict over a slave girl and then everyone hated Imam Ali for taking booty" took place long before the last hajj. And that when Imam Ali was returning from yemen and met the Prophet at ghadeer was different account. So I was told that sunnis are kinda like combining two separate event into one to make the narrative that Ghadeer Khum was about friendship.

1- Most historians state he went two times while some historians state he went three times to Yemen.

2- The first was year 8 while the second was year 10. Those who add a third state it occurred between year 8 an 9.

3- Yes you are right. The objecting and complaining took place only during the first one (year 8) not he second one (year 10). Sunnis have conflated these two to undermine Ghadeer.

If you read Arabic, you may read this short article:

https://www.aqaed.com/faq/1095/

And also this part of the book اعيان الشيعة which is more detailed:

http://shiaonlinelibrary.com/الكتب/3636_أعيان-الشيعة-السيد-محسن-الأمين-ج-١/الصفحة_405

And you can read some more details here about the first trip:

https://www.aqaed.com/shialib/sia06/6.html