Can I keep a Bitcoin Core wallet in an external hard drive ?
Yes you can. Note that your "wallet.dat" is only a few MB, the full blockchain is close to 200 GB now.
If yes do I only need to copy the directories or I can install it in it just like can install for example a game to use in my PC directly from this external hard drive ?
This will depend on your OS, assuming you use Windows, I can't tell you
How much of a size should I buy the hard drive in order to keep the Bitcoin Core there for at least 10 years, 4 TB ,8 TB or 16 TB (not sure if there are 16 TB external hard drives here) ?
The Bitcoin blockchain grows approximately 1 GB per week, maybe more if you store full SegWit blocks.
I wouldn't assume your hard drive will last 10 years (backup your wallet.dat!), and suggest to just get 1 TB at most. By the time blockchain fills it, new drives will be much cheaper again.
Note that using an external drive in different computers risks exposing your wallet to more malware.