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Your pants!
Yes, Lavender and gray match quite well.
A strict match of navy pants would be navy or black shoes. Otherwise, you could look snappy with a red blouse and red shoes.
Yes your shoes should match your shorts or top
No, you should always try to match your belt and shoes, i.e. black belt with black shoes.
While wearing white sequin shoes you may want to wear a matching blouse or dress that also have white sequins. You may want to try a matching handbag with a sequins design that would also match your shoes.
Wear socks to match the pants
Ones that match..
Beige
Not really. Sometimes being different can be interesting.
Your shoes should match your belt. I would go with black.
Mahogany is a shade of dark brown. You should wear whatever color socks that match your trousers when wearing mahogany colored shoes.