In answer to your first question, I think a big problem in davening that affects everyone is that since people cant see Hashem, and the answers to our Tefillos aren’t always the ones we want/are looking for (so we don’t see the answer) we get discouraged. I think one way to change this would be to talk to Hashem throughout the day. “Hashem, thank You for letting me catch ABC before he/she went out.” “Thank you for letting me get to the cleaners before they closed.”… simple things like that. It will strengthen your relationship with Hashem and make davening easier for you (and seem like less of a “burden”). Also, dont forget that Davening is for your good, no one elses. And remember that the better your life will be the stronger and better your relationship with Hashem. (Not talking about the actual events of your life, but you will have a very good attitude which will make your life better.)
For the second question, I’m not an LOR but ask yourself if you sincerely want to be a good davener. (And based on this thread, I would say the answer is yes.) If thats the case, “Mitoch Shelo Lishmah, Bah Lishmah”. (If a person wants to do something for the right reasons deep down but they get “covered up” by other things. Eventually the right reasons will shine through.
Hatzlacha Rabbah!