Supply and demand is one factor, but here the bitcoin is not like other currencies, it is not regulated so the supply and demand doesn't impact it that much. Major trading is one of the major factors that determines the bitcoin price. There are other factors too, technological advancement which can only be accessible with bitcoin give bitcoin a huge boost. By technological I mean that you can save your money in your PC and this is a big advancement in technology. This only is reason enough for the price of bitcoin to be up or at least a bit more than gold.
You forgot about the fact that mining difficulty increases over time and this results in the need to get bigger mining rigs and hardware and makes it harder to acquire Bitcoin in general which leads to the price increases like we are seeing today.
Is the fact that between mining difficulty and transaction fees have a relation? We've seen the bitcoin take a new ATH this week, but then, users are talking about the transaction fee also increase that must they pay for every transaction. Do you think there a relation between both things? more higher the bitcoin price, the lower the transaction fee, why doesn't like this.