Good grief, Chloe - your bank needs a new translator..
All three of the attempts above (from you and your friends) are much better than the bank's attempt and each has some good points about it, but none are actually entirely correct.
In Mark's sentence, "from buying financial products which are not permitted by this bank," is good English.
In Helen's sentence, "buy unauthorized financial products through channels not authorized by our bank,," is also very good.
And in your sentence, both the start "The client who purchases financial products which are not permitted," is good as is "from informal channels should bear all the consequences." But you went wrong in the middle.
To judge from the replies that the three of you have posted here, my best guess as to what the translation should be is:
"Any unofficial products that are bought without permission from this bank, are bought at the buyer's own risk."