How does aluminium amalgam work as a reducing agent?
Could aluminium amalgam be used to deoxygenate a carboxylic acid or amino acid to the corresponding alcohol or alkane? 


No. Aluminium amalgam has been used to selectively reduce other groups in molecules containing a carboxylic acid group, while preserving the carboxylic acid group.  

See for example in Industrial Organic Nitrogen Compounds at page 139:


  Some pyridine-carboxylic acids have been reduced to the corresponding dihydropyridine-carboxylic acids with aluminium amalgam.


See also the patent Polyene carboxylic acids and esters and manufacture thereof where aluminium amalgam is suggested as a mild reducing agent which preserves the carboxylic acid or ester group.