MacBook Pro - will 10 hours of continuous fan usage cause damage Is it OK to run a MacBook Pro (late 2013) for 10 hours continuously with fan? 

I am thinking of turning it into a local Android build machine. It has a 2.4GHz dual-core Intel Core i5 processor which means it takes about 8-10 hours to compile my Nexus image (depending on if I have other programs open). The CPU does get hot - close to 90°C. 

I have raised the whole body by keeping it on some plastic feet. 
I am worried if the heat will destroy the logic board or fan will fail soon.
You should be fine. 90°C is not that high for a CPU that's under heavy load. I've seen MacBook Pro CPUs run as hot at 117°C when under heavy load.

As a point of reference, you can refer to the Intel Mac Temperature Database to get a sense for how hot MacBooks can run. You can search and filter the results as needed.

As for your concern that the heat will destroy the logic board or fan will fail soon, these are things that can happen unexpectedly to any computer. However, I wouldn't be worried on the basis of a CPU that runs close to 90°C under load. And, at the end of the day, a computer is a tool and if you need it to be an Android build machine, then that's what you need to use it for. As long as it runs the software and produces the results, then it's capable of doing the work.

And, as always, make sure you have a backup regime in place!