is there a way to get no dwarves but a good amount of every other race?
If you try to make dwarves extinct by high amounts of beasts/savagery it is usually difficult to keep elves alive since they are so incredibly squishy. Your best bet would be to generate a world that has very few mountains but many forests. Set the number of sites to something high. It will take some tries but you will get there eventually.
Alternatively you could make dwarves sterile in the raws for example by adding
[ORIENTATION:MALE:100:0:0]
to the female caste. Generate a world with, say 200 years of history, and dwarves should have died out barring the occational vampire/werecreature/necromancer. Before you embark, reset the orientation to normal so your fortress dwarves are not sterile as well.
As an add-on to this question, is there a way to embark without selecting a dwarven civ, even if there are still existing dwarf civs?
No, you always have a home civ, even if it is a dead one.
is it possible to become the mountain home if you are the only site left
Yes, actually when embarking from a dead civ, you will become the mountainhome immediately at embark or shortly after. One of your dwarves simply becomes the king.
Besides this is basically the only actual game-play effect that embarking from a dead civ differentiates from setting a low population cap, as even a dead civ will still send caravans for some reason. There won't be a liaison though so you won't be able to negotiate trade agreements.
If you really don't want any interaction with your home civilization - dead or not - embarking on a small island is the only possibility I am aware of. Unfortunately that will also cut off all the other civs. Maybe some better options will be available with the starting scenarios in the next release.