1. Physical attendance during term time yes, but that's only half the year. My children are both at college studying degrees overseas, they are there 6.5 months of the year and come back home for 5.5 months of the year during school breaks. So where was he during school breaks and how can you prove that?
2. Agreed, but that's not enough for you to obtain citizenship through him.
4. Photos don't help, he could have been visiting. How about sworn affidavits from your siblings stating he was there for a certain amount of time?
The issue you've got is that he could have got citizenship with only 30 months physical presence, but then wouldn't have been able to pass his citizenship on to you. So you need to find stuff that shows he was unequivocally in the US for the 5 years required, and what you have so far doesn't seem to do that.
Again, how did he get citizenship? He must have been a green card holder so how was that obtained, do you know? And for the 'certificate of movement', how much time in the US does that show?
Just trying to help with picking holes in it so that you can fill them if needed!