well, if you really want to translate into french the current act of doing something, you have to use EN TRAIN DE. This translates exactly i am drinking. je suis en train de boire..... every time you have the english progressive form, you can use EN TRAIN DE . i.e. je suis en train de, tu es en train de etc, for any verb. I am a french native'speaker.
Mon, ma and mes are my. Ton, ta and tes are your [singular, familiar you]. Son, sa and ses are his/hers/its/theirs. Notre and nos are our. Votre and vos are your.
Mon/ton/son are used when the owned object is masculine¹ singular. Ma/ta/sa are used when the owned object is feminine singular. Notre and votre are used when the owned object is singular; they don't change with gender. Mes/tes/ses/nos/vos are all used when the owned object is plural; likewise, they don't change with gender either.
¹ And finally, just to make it even more confusing, ma/ta/sa all become mon/ton/son when the feminine singular object begins with a vowel sound. E.g. it's "mon amie" for my (female) friend. If it helps, when you try to use ma in this situation, it'll just sound wrong to you. "Ma amie" is much more difficult to say, so the French switch to mon.
Ton is when you are talking to someone you are familiar with - it goes with 'tu'. However, 'votre' comes from 'vous', which is used when you're talking to someone you're not close to, or when you are addressing multiple people. (In this case, 'ton' is probably used because if you are stealing someone's coffee then you probably know them pretty well.)