My corrections,  PPaulo did a great job, but these expressions are not easy to understand and remember.

to be on record, to be on file, to be on report  (Three possibilities with different meanings.)

to take priority
 
to be free of charge, to be free of cost
 

to drop a hint
 
to let yourself go    (PPaulo is right.  Mary let herself = Mary did not take care of her health, weight, etc.) 
 

to carry out instructions

to be under guarantee (The guarantee is still valid.)

to offer/promise/dedicate something to someone 
 
to show/feel/take pity   

to watch your step    Or you can slip someplace..  (But also "to be careful" in general.  Watch your step or I will steal your girlfriend,)

to put in a good word about/for someone (to recommend)

to confirm or deny

to catch a lift (carona)