~~ Is Bitcoin more convenient to use?
~~ Is Bitcoin easy to use (How can we make it easier to use?)
I united these two because they seem to be about the same thing. Convenience is a matter of interface and devices that can be introduced to utilize payments. If it's implemented in a 'pay with your smartphone' kind of solution, it is/will be convenient. Moreover, it's a matter of habit, so it might not be easy and convenient to use Bitcoin at first but people can come to like it when they get used to it.
~~ Is Bitcoin cheaper to use and where will that solve problems?
Yes, if we are talking about big transactions. It can solve problems of SWIFT-like money transfers or transaction fees when spending money on a big purchase ($200+).
~~ Is Bitcoin safer to use than traditional payment options? Where will it be safer to use?
Yes, it's safer everywhere you use it.
~~ Is Bitcoin faster than other payment options? (Where can we apply it to solve problems with other slow payment options?)
Well, it can be faster than international bank transfers, but it's way slower than instant transactions with fiat.
~~ Are we using Bitcoin for the correct applications? (Trading or Currency) What should we focus on?
I think we should focus on currency, but that means we need to solve some serious problems.