Dance pPerformance will start.Starting Soon Dance Performance Starting Soon

Looking at the entire piece of writing, this feels like an appropriate title. We usually do not use a full stop in titles.

I"'m waiting for my daughter's dance performance right now. I'm waiting for my daughter's dance performance right now.

An apostrophe ( ' ) is what you use for contractions like "I'm" and possessive marks like "daughter's".

I"'m waiting for my daughter's dance performance to begin right now. I'm waiting for my daughter's dance performance to begin right now.

You need to specify whose daughter it is, so you should include "my".

My daughter is looking forward this event, and I'm really looking forward it too. So am I. My daughter is looking forward this event. So am I.

Actually what you originally wrote was grammatically correct. It's just that it feels repetitive; to keep it nice and simple, "So am I." is how you indicate that you feel the same way. (If it helps you remember, it acts a bit like 「私も」.) "Me too." is a frequent alternative.

My daughterShe is looking forward to this event, and I'm really looking forward to it too. She is looking forward to this event, and I'm really looking forward to it too.

Since you've mentioned your daughter already it's clear that "she" would refer to her. "looking forward" requires "to" after it.

I really feel that a child’s growth is happy foa source of happiness for their parents. I really feel that a child’s growth is a source of happiness for their parents.

I really feel that seeing our child’ren's growth is a happy thing for parents. I really feel that seeing our children's growth is a happy thing for parents.

This is a general statement, so should be in plural. Adding the word "seeing" here means that you are observing the growth (because you cannot experience the growth yourself, you witness it).