If you want to suppress this functionality as a BAPI you have to wrap the functionality in a Remote Function Call (RFC) module. Just implement a RFC function module. Depending how the report is implemented, it may use ABAP objects, which can also be called from your RFC implementation. Given that case you have a quite good solution. Whenever the report is adjusted, also your BAPI will reflect the changes. In case it's a standard programm from SAP which cannot be wrapped, think about copying it into your namespace and adjusting it. Nevertheless this might give some hassle, when SAP performs an update via Support Package Stack and you won't realize it. The output of the two methods is different. Apart from that, if you want to call it from outside, there is nothing else possible than implementing a RFC module.
A submit report can not return the values outside. Reports are always only for GUI functionalities and not for exchanging data. In case your report uses select options, you somehow have to implement this feature "by hand" in your RFC, as this statements can not be used inside RFC modules. I would generally try to rework the report, modularize it and put the selection information in a central class or maybe another function module wich can be called from the report and your BAPI function module. The filters you are talking about can not be implemented in RFCs automatically. You have to implement those ranges manually. The warning which comes up cannot be suppressed, if you do a RFC call from a remote system and the popup with the warning comes up you'll end with a shortdump. Therefore, you have to rework the report and to re-implement it for your needs.
If you are just looking for bypassing it via job scheduling, create a variant and schedule the report with that variant but I suppose that's not the solution you're looking for.