8
What is the largest number of blocks a transaction has ever waited before eventual confirmation?
Please exclude:
Transactions with very low fees and or/are dust amounts acceptable. Please link the txid if available
6
This is not a full answer, but a partial answer somebody may use as a stepping stone to craft a complete answer.
E.g. blockchain.info shows both "received time" and the time of the block a transaction was included in. 
It appears to me that the "11 minutes" in the "Included in Blocks" time for this transaction corresponds to the difference between "Received Time" and "Block time" of the first confirmation.
If this information is available on blockchain.info's API, someone could parse all transactions to find the maximum.
By additionally evaluating the fee of a transaction in comparison to fee levels at that time, and confirmation times of each input of the transaction, the additional constraints of this question could be addressed as well.
4I'm not sure how anyone could get this sort of data. There would not be any information about when a transaction showed up in the mempool, for example and wasn't included unless you have miner logs. – Jimmy Song – 2016-06-12T11:05:50.200
Low-fee transactions can be unconfirmed for a very long time. For example, this one https://tradeblock.com/bitcoin/tx/7da5cb18d48179ecdb9bbb61ab040d3846669c328d5ab58ff560ec150a021e36 remains unconfirmed from october'15 and this one https://tradeblock.com/bitcoin/tx/c1320985118aaa2aacaef7deba125de52d368bbe86bbf221ff2035b935f240ca was confirmed after ~8 monthes
– amaclin – 2016-06-14T10:35:02.190