so I can conclude that if I pay a solid fee amount and wallet is not faulty, the odds of the transaction being confirmed are > 99.99%?
This is pretty much a guaranteed transaction as long as you provide a sufficient fee for your transaction. Just be careful how much you will put on as a fee as you might end up having your transaction not being taken by any miner because of having a low fee. If you want a good estimate on how much Bitcoin/byte you can give and the time estimated that it will be confirmed you can go to Bitcoin fee calculator websites such as this
one as a basis on which you think is an ideal fee as well as the waiting time you can stomach in for the transaction, you should take note that this are just rough estimates and it might not give you the expected time of your transaction being confirmed.