Hello, King Graveth has just offered me my very own castle. Unfortunately, I do not want it, however I want its town. If I accept the castle, will I receive the town, or will the town go to another lord?
No, castles and towns are separate fiefs. If you turn down the castle there is no guarantee you will get the town, although considering the number of fiefs you own is considered in the calculation to determine which Lord of a faction a captured fief goes to, turning it down couldn't hurt your chances.
In other words, you could indeed get a castle and a city, but if you have set your eyes upon a city then I'd advise you to say "No thank you" to the castle. This will make it much more likely that you will get a city.
It depends on what you call town, though from your wording I guess it's what I call village (these things you can't conquer but plunder).
If you get a castle you also get the attached village.
If you get a city you don't get the attacked villages, these go to other lords.
If you get a village you will loose it if the city or castle it is attached too is lost to the enemy.
At the start you always get only a village.
When the kingdom acquires new property (conquered castles and cities) these are given out as fief by the king. If you want the exact mechanics for this you can find them in TheMageLord's tweaks. Basically the comparison involves already owned fiefs, renown and standing with the king and who conquered it gets a bonus.
So usually the new fiefs go to the lords with the fewest fiefs, better build up your renown.