Speaking of the testnet bitcoins, the wallet address posted by the OP start with "mk" not even 1. Does this mean there's a particular wallet which are use for the testnet bitcoin or every BTC wallet are good to go?
it is not "mk" it is "m" and it is the well known initial character of a testnet address equivalant to mainnet addresses that start with "1".
https://en.bitcoin.it/wiki/List_of_address_prefixesas for wallet, usually it is developers who need testnet coins to "test" their own system so most don't need a wallet and instead use their own code.
You'll need to simply run bitcoin core with testnet=1 (edit bitcoin.conf), and then it'll generate testnet adresses, (which have a different prefix.)
With electrum you also simply add --testnet as a parameter and it should start in testnet mode. (Newer versions of electrum automatically come with a shortcut for testnet, on windows at least.)
you can run core with -testnet argument through command line too.
and you can create the shortcut of both on your system by adding the argument at the end of the location of the executable. on windows right click on the shortcut and select properties. in shortcut tab there is a box called "target" which has the directory like c:\.... at the end of it you can add that argument:
"C:\Program Files (x86)\Electrum\electrum-3.3.6.exe" --testnet
[code]
[/code]