You can send the same PCB to multiple PCB assembly companies.
PCBway only require the MPN (Manufacturer Part Number) in the BOM. You do not need to specify the purchase location.
You can add it by all means but they will probably have some stock already that they will use or buy it from their own suppliers.
To edit the BOM, open it in Excell or whatever spreadsheet software you have, add a column and then for each line paste in the URL.
They will probably ignore it.
JLC does not accept customer-sourced parts so you won't be able to send them parts to place on your assembly job.
There is also very little price difference between 50 and 100 or even 500 when it comes to passives.
Sourcing yourself won't be any cheap at 50-100 quantities. Trade companies get at least 10% off at some suppliers and 20% off at others even at smaller quantities. You have to factor in shipping the goods to China as well which is a pain to do with customs being tight.
PCBway can accept parts from customers, or source themselves, or a hybrid of both. I recommend letting the PCBA company source parts for you as they have buying power and know what format they want them in to run on their assembly line.
Both PCBway and JLC only need the Gerbers, BOM and Pick and Place files.
There is no difference between them other than JLC having a much more low-cost setup where they pool many boards together and run them at the same time through many machines.
This is why they are so cheap but you give up being able to have any sort of component that they don't stock from LCSC or are willing to buy in for you.