2 Problems: A tree and flooding

Hi Forumers,
I have an IP at Narellan in NSW.  Its in a nice area, but is on the low side of the street, half way down the hill on the outside of the corner.

This has led to:
1. Flooding.  The water runs down the street (only in heavy rain), jumps up my driveway, down the drive, the poor little gutter in front of the garage cannot handle so much water and so the garage gets flooded.

Question: Is this a council responsibility due to where the water is coming from?  We have already looked an increasing the drain, etc but it wont fix the problem (if even a bigger down pour occurs).   I think the best solution is for council to re-do my driveway entrance so its higher, thus deflecting the water further down (someone elses place will flood then! – Kidding).

2. A big gum tree in the front yard.  Not on council land is getting old and a few big branches (killing size) have fallen so we should either get the tree prunned or removed.  I figure this may be at my cost so I would go for removing.  Can council help with this?  Or if I go with removing and council say "No" does this then make them liable to fix the current unstable situation?

Many thanks for all responses (happy for the lateral thoughts as well!),
Mat