Q. I have been struggling for some time with questions such as: Is everything pre-determined?

Do we have to accept that everything is pre-determined and occupy ourselves with devotional service while still performing our duties?

Or do we have to strive toward a goal (even if that means being competitive) while still performing devotional service?

A.  If I understand correctly, it seems that your question focuses on whether or not someone performing devotional service should strive to achieve something in the field of their occupational duties or in some specific way strive to improve their present life situation.

Devotees also have goals and aspirations that they strive towards, but their impetus is simply to please Krishna and increase their devotion  and not the achievement of any material objective in itself.

In the course of trying to cultivate our Krishna consciousness and steadily progress towards the spiritual plane, we are advised to carefully perform our prescribed occupational duties and so we do. In the course of executing duties there may be standards to achieve and milestones to be reached. Our acharyas recommend that devotees should live very simply but whatever is needed to perform one’s duties nicely, one should strive according to their best capacity and to dedicate such endeavors and all facilities provided for that service fully unto Krishna. While working industriously the devotee also knows fully well that the result of one’s endeavors is in Krishna’s hands, not merely a product of their personal efforts. 
Finally, there is a clear connection between devotion-based endeavors and the notion of predestination.

As concluded in previous Digest discussions, our past actions “pre-determine” our present circumstances in life  but they do not pre-determine what we choose to do now. Our present choices determine our future. What we choose to do now can be executed on the material plane (deliberately or mindlessly, impelled by past conditioning), yielding temporary material results; or our present choices can be enacted on the spiritual plane, thus lifting us completely out of the cycle of karma. In other words, a devotee is neither directly interested in changing his/her karmic destiny nor overly concerned with improving his/her material circumstances per se, simply for sake of material welfare; however he/she is keenly interested in cultivating their relationship with Krishna. The devotee is contented to base their spiritual endeavors upon whatever position or within whatever circumstance of life they find themselves. In turn, Krishna takes charge of such a surrendered devotee  and their life is orchestrated by Krishna  and not karma.