Wasn't it said in the book that Hagrid kept pieces of his wand in his pink umbrella?

Yes, it was in his umbrella, but according to HP Wiki,

Following his expulsion, the Ministry of Magic forbade Hagrid from practising magic and destroyed his wand. Albus Dumbledore nonetheless convinced then Headmaster, Armando Dippet, to give Hagrid the job of Gamekeeper and allow him to remain a resident of the school. Hagrid continued to do magic using his pink umbrella, which most likely contained the broken fragments of his wand, or perhaps even his entire wand intact, reconstructed for him by Dumbledore using the Elder Wand[11].

So, sure, it's possible.

Yes def he still used his wand in his umbrella.

maybe yeah!

i dont think he did because in the books it says that hagrid kept the 'broken parts' of his wand in the pink umbrella

^ Harry did not know about the Elder wand intell the last book.

it was possible, as the Elder wand could do pretty much anything, and we even see it repairing another broken wand once. I guess Dumbledore didn't do it because it didn't occur to him, or because he didn't want to get into trouble with the ministry if they found out (which is more unlikely if you ask me)

sure

I don't think the books ever mentioned there being specifically broken fragments of wand in the umbrella. All the books mention is that he uses the umbrella to do magic the way other people use a wand.

I'm pretty sure Dumbledore did secretly fix Hagrid's wand, since he was convinced of his innocence but couldn't prove it. After that Hagrid had to hide the whole wand in his umbrella.