Yes, if you wash for Hamotzei it covers drinks as well (except for certain wine in certain situations, but I will not elaborate on that now). The reason is because it is part of your meal, and the making of HaMotzei exempts the entire meal, as all the food is "attached" to the bread.
The only exceptions would be things that aren't part of the meal, which brings us to your next question.
Dessert is technically not part of the meal, so it requires its own Bracha. The only exceptions to this is [certain]cake, which is covered by the Hamotzei regardless of it being not part of the actual meal (And even for cake, there are certain Poskim that require a Bracha. We will not get into that discussion now though).
Also Ices (and according to Rav Moshe Feinstein Zatzal , ice cream as well) is considered a "drink" and not food and does not require a new Bracha, as drinks are always considered part of the meal. Nuts, fruit, popcorn, potato chips and candy do require a new Bracha.
Vegetables arent usually served for dessert, so they are part of the meal and as such usually do not need a new Bracha.
Keep in mind that even though a Bracha is necessary,a Bracha Achrona is not necessary as the Birchas HaMazon will exempt all that you ate.
Important Numbers
