Today, I came across a user who posted lots of question in 1 area with no attempts on any of them. Many of these were very good questions and have answers. I would certainly benefit from learning from them, on the other hand, the user clearly made no slightest attempts on what appeared to me assignment questions? As a consequence, I favourite questions I down voted. (Because someone already provided a good answer) just wonder if I am like one of the only people who have ever done this... This is somewhat ungrateful, I thought...
Marking a question as a favorite basically says that a particular user feels like watching that question. It's completely separate from the voting system
Being the only built-in way to keep track of changes to questions, favorite could conceivably be used for both good and bad questions. There are various reasons why one might want to follow activity, including edits, on a question. One reason is that one may want to reverse downvote or retract closevote if/when the question is brought into shape.
Briefly put, I don't see a contradiction between downvoting and favoriting (=bookmarking) a question.
But in your concrete situation, given that
Many of these were very good questions and have answers. I would certainly benefit from learning from them
I think you could consider recalibrating your criteria for downvoting.
(This is coming from a user with downvote per day ratio of over 20, top on the site.)
I tend to downvote problems that look like they were copied straight from a textbook, like "Evaluate ..." Doesn't mean the problem itself isn't interesting or I couldn't learn from it, in which case it would still be worth favoriting. Or maybe a bad question has an insightful answer that would be worth referring to again.
Of course, if you feel guilty, it always helps to provide a reason for the downvote so they can avoid more downvotes in the future.