Dreams about family gatherings, such as parties, often reflect your feelings and relationships with those family members in waking life. In your dream, it seems that you are processing both your connection to your father and the significance of family celebrations.

Here are some possible interpretations of key elements in your dream:

1. Your Father's Age: The discrepancy between the age you thought your father was turning (82) and his actual age (84) could suggest feelings of uncertainty or confusion regarding your relationship with him or perhaps the passage of time. It might also indicate a desire to hold onto memories or moments from the past, as you seem to be reflecting on his life and experiences.
2. The Party Setting: The large venue with dark wood elements may symbolize tradition and stability, possibly reflecting your family's heritage or the importance of family gatherings in your life. The private dining room could represent intimacy within your family, suggesting a desire for deeper connections with your relatives.
3. Your Role at the Party: Arriving early but not participating in the setup might indicate feelings of being an observer rather than a participant in family dynamics. This could suggest that you feel somewhat distanced or separate from the activities of your family, or perhaps you're more comfortable taking a supportive role rather than being in the spotlight.
4. Finding a Bathroom: The search for a bathroom can symbolize a need for personal space or a desire to 'process' your feelings. Bathrooms in dreams often represent a place to relieve oneself of burdens or emotions.
5. Interactions with Family: Your brief chats with your father, particularly at the juke box, might represent a longing for connection or communication. It indicates that you cherish the moments you have with him, even if they're fleeting.
6. The Coolers and Snacks: These elements may symbolize abundance and the importance of sharing. Helping someone find a drink could reflect your willingness to support and care for your family, highlighting your nurturing side.

Overall, this dream may suggest that you are reflecting on your family's dynamics, your role within it, and the importance of connection, especially with your father. It might be beneficial to reach out to your family members and engage more deeply, especially as your father's birthday approaches. This could strengthen your bonds and create lasting memories.