How to discourage rats

Hi!

We bought these RSPB Coconut Suet Treats. Birds love them. Problem: rats climbed up, gnawed through the string, and ate the suet while the coconut was lying on the ground. After the first time, I hung the coconut again using a plastic zip tie, but it was also gnawed through and the coconut fell down. We have taken the coconut treat inside for now. Here is a picture marking the spot where the treat had been hung initially.

Question 1: how can I hang the coconut so that it is safe from rats?

I'm considering the spot on the right marked in the picture, hanging from a tree. But I fear rats will be able to climb the tree and repeat taking the coconut. 

Question 2: if I hang the coconut under such a squirrel baffle and make sure that there are no branches underneath the coconut, will the coconut be safe from rats?

We also have a bird feeder. It's pictured in the second photo here. Birds spill seeds when eating from it. I think that also attracts rats.

Question 3: what do you think of covering seeds in chilli oil (as recommended here)? I think rats and squirrels wouldn't eat spilled seeds then. I think dusting seeds with cayenne pepper would stop squirrels and rats from eating from the feeder directly, but they would still eat spillage.

Alternatively I can imagine fitting a squirrel baffle on top, and a plate underneath to catch spillage. But I have no idea where to hang this construction eventually, because the lower branches of the tree are not strong enough to hold this.