- What would you recommend for me to improve my English pronunciation?

Otras opciones:
- How would you recommend I improve ...
- What (resources (recursos), books, etc) would you recommend to help me improve ...

- If my English writing is wronghas mistakes, can you correct me please?

"writing is wrong" -- no sé por qué pero no me suena natural ... quizás porque, para mí, se usa "X is wrong" cuando te refieres a una cosa _específica_, no una cosa en general (como la escritura). ¿Me explico?

(Is there another more humble way to ask this?)

another - https://www.merriam-webster.com/dictionary/another

"another" = "one other", más o menos :-), or "some other"

Notas:
- I have the other book (otro libro específico)
- I have another book (otro libro, no específico, o un libro de sobra)
- I need the other shoes. (otros zapatos específicos)
- I need other shoes (otros zapatos -- Cualquier zapato servirá.) No se puede decir "another shoes", ya que "another" es singular.

Please, let me know if there's any mistake when I pronounce __.

either "if there's any mistake", pero mejor sería "if I make a mistake"

- What would you suggest for me to improve when pronounciating this?

O "- What would you suggest I improve when pronouncing this?"

- What would you recommend for me to improve my English pronunciation?

- If my English writing is wrong, can you correct me, please?

If my writing is wrong, would you help me correct it, please?

Please, let me know if there's are any mistakes when I pronounce __.

- Does it/this sounds natural to you?

- What would you suggest for me to improve on when pronunciating this?