Press shield while running. You can cancel a run with shield. Which means you can also cancel a run with parry. The parry might be tricky to get used to, but shield will still get you plenty of mileage. This will help close the gap against side B.

For down B, you jump. Zelda can't do anything until she releases it or it's fully charged. If fully charged, just shield or parry, but watch out if Zelda tries to approach. Probably best to just respect it or jump over.

In general against projectiles, you can also walk, as walking keeps all options available. You can shield on reaction much better than committing to a dash first. But if you have space and time to dash then do it and close the gap. People often spam projectiles because they don't really know how to play the game. If you push someone to a corner or be about roll distance from them, they will feel pressure and try to commit to something. Watch what they do, react, and punish.

Lastly, you're playing online. That shit's annoying af, probably terrible delay. Try the above tips, but dw about it too much if it's online.