My idea is to simply install Bitcoin Core 2013 version in other folder, and it should use the /.bitcoin folder to get the block files. But my concern is that instead of using the existing files, it's going to do something to the files or something that forces me to validate or even download the entire chain again which is hell.
Your concern is correct. Looking at change log on older version of Bitcoin Core, there are several change to format of block database format and chainstate.
The first time you run version 0.15.0, your chainstate database will be converted to a new format, which will take anywhere from a few minutes to half an hour, depending on the speed of your machine.
The file format of fee_estimates.dat changed in version 0.15.0. Hence, a downgrade from version 0.15.0 or upgrade to version 0.15.0 will cause all fee estimates to be discarded.
Note that the block database format also changed in version 0.8.0 and there is no automatic upgrade code from before version 0.8 to version 0.15.0. Upgrading directly from 0.7.x and earlier without redownloading the blockchain is not supported. However, as usual, old wallet versions are still supported.
I want to do this because I want to convert a 2013 wallet into the new format. And I want to do it with testnet coins first, so I don't screw up with real coin wallets. But I need to download Bitcoin Core 2013 first to create a 2013 .dat wallet file. Then I want to be able to migrate it into the new format, and then create a watch-only wallet for an online node in another laptop.
Just like @BitMaxz, i'm somewhat confused and don't know your exact goal. But i'm fairly sure even older version of Bitcoin Core let you create wallet.dat file without performing sync/IBD.