Does anyone have any experience of flying Air Baltic on BA flight numbers?

I have Jersey London then London Riga return tickets.

Choosing seats and check in
Manage my booking in BA App is not allowing me to choose seats " this will be available at check in" I go to Air Baltic site and it doesn't recognise my booking number. Will I have problems checking in? Will I check in and choose seats using the BA app ?

Checked Luggage
The information in manage my booking is confusing. It says I get my usual allowance on the Jersey London but on the Riga flight it states just 1checked bag. On air Baltic some ticket categories get a 20kg bag others don't. Can I assume that I have a checked bag?

The reason I ask is that others in TripAdvisor etc have experienced problems, incurring unexpected check in and baggage fees of substantial amounts.