Assalamu alaikum, fellow Muslims, I'm new and could use some guidance on prayer and wudu

I recently embraced Islam (said my shahadah alone) just a week ago, and I'm slowly trying to learn the ropes. I'm eagerly waiting for the Quran I ordered a few days ago to arrive. Learning the prayers is challenging, but I'm determined to get there. I do have a question though-I learned that wudu is necessary before each prayer, but I'm a bit confused. Do I really need to wash everything three times, like using soap for my hands three times? The water in the nose part seems a bit tricky for me, but I'll do my best. If I skip wudu, does that mean my prayer isn't valid? Also, if I practice praying or pray before I take off my fake nails, is that acceptable, or does it not count? Any advice would be appreciated, jazakallahu khairan!