I've been stuck on the last four for ages, so I'm swallowing my pride.
1d. Knight errant employed by weak emperor (6). KEMP-R
7d. Saw tot running into station (6) STA-DA
10d A female supporter turning up in carriage (4) ARB- ( a bra backwards, sure, but an arba carriage? What can that be?)
32a Bird creating kerfuffle in part when losing tail (7, two words) S-ADA-E (I suspect that this is not an obscure archaic Outer Mongolian expression so should be easily doable but it has stumped me all day)