Need help.

[praetorians cavalry]

Hi.There is something I want to ask you guys.May I have your help?
1)Earning the Senate's favour give you what benefit?I cant tell,maybe with high standing in the Senate you can take Rome without being declared outlawed?As far as I know,when your empire gets large and powerful the Senate always hate you and want to weaken you.I cant manage to keep my standing with Senate high,only the People help me take Rome.
2)What is improving general's body guard?When I read the text for a Governor House, it says this building can improve the body guard of your genaral.But my general unit in that city doesnt change any.All of his stats remain exactly like before.So what is the improvement?(retraining doesnt work)

[Sinner]

The higher the Senate's favour, the more likely you are to have family members voted into one of the various Senate offices, which all give nice stat benefits, plus in some cases can enable you to avoid penalties for failed missions.

The improvement to your leader's bodyguard that you gain from the highest level of governing building your faction can build is the number of men in the bodyguard. The upper limit to the bodyguard otherwise seems to be determined by the leader's stats and retinue.