Druidry as a spirituality can stretch from a full religious (druidism) to a more philosophical approach to nature. I myself am a pandeistic druid. I feel like agnosticism fits as well.
Absolutely. Many deities are non-binary. I tend to use the word deities rather than gods and goddesses for that reason.
Paganism is a very large grouping, including witchcraft, Wicca, Asatru, heathenry, some branches hermetics and gnosticism, many syncretic faiths such as Voodou, Santeria and some cultural approaches to shaman-like traditions (and you will find many that argue for and against inclusion of many of these). Druidry is more traditionally focused on pre-Christian Celtic religion and spirituality and is largely a constructed path based on conflicting sources. Again, the reading list above is an excellent resource.