The long run is defined as a period in which all INPUTS are variable. Because of that all costs are variable too.
You're right that in the short run your rent and the cost of the machines you've already bought are fixed costs. But in the long term they aren't.
In the long term, you can buy or rent a larger building (as you expand your company). Then that cost would go up compared to now. You can buy more machinery and the same thing would happen. You can change anything because ALL inputs are variable.
So even those things that are fixed in the short run become variable in the long term.