Separate dataframe for every sheet:

with pd.ExcelWriter('output.xlsx') as writer:  
 
     df1.to_excel(writer, sheet_name='Sheet_name_1')
     df2.to_excel(writer, sheet_name='Sheet_name_2')

For width, but I never used that:

df.style.set_properties(subset=['column'], **{'width': '300px'})