5
In the past it was possible to get a transaction without a fee confirmed if the inputs and outputs had a high enough priority and followed some rules. As of 2017 is a "free" transaction still possible if you don't care about how fast it will be confirmed? Several hours or even a day or two would be acceptable.
4
The Bitcoin consensus rules do not require transactions to have a fee, so it's still theoretically possible for a free transaction to be confirm.
It is, however, unlikely that any miners today will confirm free transactions. You can test this by sending yourself a free transaction to see if it confirms (but be sure you use a quality wallet, such as Bitcoin Core, that has features for handling transactions that never confirm).
-1
Yes. It is possible. But what exactly do you want to achive? Either you want to minimize the fees or you want to delay transaction confirmation. Difference in details...
2For the record: I created a free transaction that got confirmed in about an hour (maybe lucky?). The transaction was within the rules mentioned in the question. – tlo – 2017-01-14T13:43:33.137
@tlo: how did you resolved/avoided the "error code: -26;error message: 66: insufficient priority"? – V-X – 2017-03-10T22:39:58.477