Not sure of syntax or why 3rd person is used

Can anyone explain the syntax - I guess it’s idiomatic Latin or some such - of this.

Davus asks Quintus - who is ill with a sore foot and a sore head - how he is:

Quintus: Quomodo se habet pes tuus hodie?

I’m not sure of the syntax and why it’s in 3rd person. Does se habet refer to his ‘pes’ - i.e. 'How is your foot doing today?

Actually perhaps of more interest is - can anyone explain the case of ‘tuus’. Why isn’t it ‘tuum’

Yes, exactly.

Bene mē habeō: “I have myself well” = I am well.
Quōmodo tē habēs?: “How do you have yourself?” = How are you?
Quōmodo sē māter tua habet?: How are your mother?

Etc.

Quintus: Quomodo se habet pes tuus hodie?

I’m not sure of the syntax and why it’s in 3rd person. Does se habet refer to his ‘pes’ - i.e. 'How is your foot doing today?

Pes tuus is the subject of habet - how does your foot have itself today? How does your foot fare today?

Actually perhaps of more interest is - can anyone explain the case of ‘tuus’. Why isn’t it ‘tuum’

Pes is masculine.