Yes, the letter 't' at the end of a word such as 'navet' is silent. The doubling of the consonant and the addition of the 'e' shows that you have to pronounce the 't'. Think of French words which we use in English, such as 'ballet' (the end of the word is 'open' ) , as opposed to 'barrette' (where the 'tte' is pronounced).
A single 's' in the middle of a word is pronounced 'z', while the double 'ss' is pronounced 'ss'. So 'baiser' has a 'z' sound in the middle, while 'baisser' has an 'ss' sound.