I am also trying to make a Deep Gnome Druid. I am having trouble with how many skills to put and what is their modifier. Also what to put for passive wisdom and how to calculate it. The players handbook tells me to choose two skills for creating a druid, but aren't there more I can choose with being a deep gnome?
It appears that Deep Gnome doesn't give you proficiency with any additional skills, just advantage on stealth checks. Note that there is no restriction on being able to use a skill without proficiency, your character would simply not be as good at it as another character who did have proficiency.
So once your ability scores are all squared away you can select the two skills your druid is proficient with as part of their class, these skills are: Arcana, Animal Handling, Insight, Medicine, Nature, Perception, Religion, and Survival.
The abilities that each skill is associated with are all listed in the players handbook but for ease: Arcana (INT) , Animal Handling (WIS), Insight (WIS), Medicine (WIS), Nature (INT), Perception (WIS), Religion (INT), and Survival (WIS).
You may also get additional skill proficiencies based on your character background. However you would not be able to pick up additional proficiencies because of the player race you've chosen.
As an aside, this thread is almost a year old, and it's generally better to post a new thread in these situations so as not to confuse your questions with the original intent of the thread.