Against backdash, I think there are a few options.
If you’re up close and have the time to set up a true meaty, st.mp, st.hk, and b.hk (axe kick) should all light up backdashes. With a counter hit, I think.
You can also walk up sweep or dash st.lk, cr.mp, cr.mk.
If you’re close enough, f.hp (rush punch) can land super meaty on a backdash, I think.
And there’s always meaty hk tatsu. I did this from a meaty empty neutral jump on a bison just yesterday after I noticed his wakeup backdash on the first knockdown.
This one is more of a read, but it can be pretty safe. Beats backdash and throw tech, can escape or avoid a hard punish if they crouch block (maybe a crouching normal to air reset you). You’ll eat a big punish if they stand block, but that’s just the mixup. Again, it’s good if you think they’ll backdash or throw tech.
Fireball can be safe, but you don’t get much out of it.
As for landing raw sweep in neutral, I try to only use it when I’m sure they’ll be walking back or forward. I like to see how they react to simple blockstrings, like st.mp, cr.mp, or cr.mp, cr.forward. If they are offensive and hit buttons or jump forward, I’ll cancel into fb to catch them or block if I think I can punish the jump hard.
After rushing people down pretty hard, I find that a lot of people will try to walk back after blocking a string to build some space. This is when I’ll sweep.