Problems installing El Capitan

No, you won't void the warranty as long as the memory modules are the correct ones & the clips aren't damaged in the module holders.

It does sound like you have a HD problem here. The standard Apple Apps should show up on the dock correctly after the upgrade. Some Apps may not show up correctly in dock tray as they are not able to run under El Capitan. If you open the Application folder for these Apps have a gray circle & bar across them these apps won't work.

But I suspect your issue is more likely a corrupted drive or the drive doesn't have enough free space. Which messed up the OS upgrade.

To start with I would backup anything important and create a bootable drive (USB thumb drive) so you can reboot under it to run Disk Utility off of it to check your internal drive. You'll want to remove anything not needed to free up at least 1/4 of the drive. you'll also want to clear out the old cache & Log files using a too like this: Disk Doctor and then defrag your drive using a tool like this one: Drive Genius

Once you've clean things up you should try reinstalling the OS that should fix things.

Do be careful were you go in India! Some store fronts claim they are Apple Stores which they aren't! Go to Apples web site to find the real Apple authorized services centers.