There is nothing wrong with a bit of animal fat. There is nothing wrong with whole eggs, avocados and olive oil. There is nothing wrong with nuts.
A bit of butter and cheese is fine.
Full fat yoghurt is great.
The skin on the chicken and the fat on the bacon are OK too. A bit of mayonnaise isn't the end of the world either.
A low fat diet is not the way to lose fat.
The very best thing you can do to aid fat-loss is ditch anything that comes in a packet or a box. The fat found in processed foods is lethal. Literally.
By cutting flour and sugar from your diet you will automatically cut out all those processed foods that cause so much damage.
It really is that simple.