My questions are
Is SQL Server leaking memory?
Highly unlikely but you should plan for SQL Server 2012 SP4 ASAP. From my past experience I could say that since SQL Server and other applications like SSAS and SSRS are all running on same machine SQL Server might be facing memory pressure and so might be the case for SSAS/RS. I have seen lot of systems like this and it all boils down to memory pressure.
You have 32 G of RAM and you have given just 16 G to SQL Server make it to 20 G and see if this help. Adding more memory would definitely help if you can go for it.
There can be plethora of reasons why queries are timing out and Troubleshooting SQL Server performance issues can help you to find the root cause of it.
But when I select memory occupied by Percentage, it shows 80%-85% which is NOT RIGHT:
I would start by saying Task Manager is not a correct place to gauge SQL Server memory consumption, it will not tell you correct value when SQL Server service account has Locked Pages in Memory(LPIM) privilege. This is because normally task manager tracks Process Private bytes memory which is pageable and allocated via VirtualAlloc() function but with LPIM chunk of memory allocation is done by AWE API which is NON pageable so task manager does not tracks it and this can lead to incorrect value. For percentage thing which you are looking is actually
Percentage of Process Private bytes not the complete memory and it does not provide any relevant information so just stop looking at it.
It is quite normal for SQL Server to utilize memory allocated to it and to know how much physical memory SQL Server is using please use query
select * from sys.dm_os_process_memory
PS: It is always recommended to move other applications on different machine (if possible) and let SQL Server run solely on it own system this will help SQL Server run faster and better