well both "uusi poikaystävä" and "uutta poikaystävää" are correct but they don't mean the same (the difference is pretty subtle). We don't know the context so both options should be fine.
"Onko sinulla uusi poikaystävä?" sounds like the speaker has found out that the person they are talking to is going out with somebody or something similar.
"Onko sinulla uutta poikaystävää?" sounds like the speaker doesn't know if the on they are talking to has a boyfriend or not and they don't have any info on the person's dating life
Yes, "onko sinulla something" can be usually thought of as "any of something".
Onko sinulla kakku. Do you have a cake.
Onko sinulla kakkua. Do you have [any] cake.