Kai's Themed Cryptic

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Across
  1. 2. Sweet found in bogus place (9)
  2. 4. I am first following winner to have cake (8)
  3. 6. Teacher messed up one north-east road (6)
  4. 8. Celt around 10 found in south London (7)
  5. 11. This lane is for the Baron's joint (8)
  6. 13. Station location follows immunisation with first ultimatum (8)
  7. 15. Bird inexperienced at park (5,5)
  8. 17. Pet shop found where woman is healthy (8)
  9. 18. Add water to cake mix for animal rescue (9)
Down
  1. 1. Cemetery has century old sap predating water source (10)
  2. 3. Ice age sloth heard English meat in woods (8)
  3. 5. An ancient sounding road (7)
  4. 7. Here, no republican would hear (7)
  5. 9. Mixed up equations with Europe's first river (6)
  6. 10. Area pet crossing (7)
  7. 12. Write German suburb (5)
  8. 14. It's gentrified how a chicken eats dried meat (7)
  9. 16. Mostly boring magician is said to be in neighbourhood (7)