I'm not sure what is it, but there is something on the lane. -- **Correct sentence~ ^^ 

Every player blocked their director from the fight. -- **Correct sentence~ ^^ 

How's going on the project that we discussed? --**Correct sentence~ ^^ 

Do you know how far out the hotel from here?

Better say: Do you know how far the hotel is from here?

The meeting is running late. I suppose the reason is finance. --**Correct sentence~ ^^ 

She already left. I think she is on her way at this point. 

Better say: She already left. I think she is on her way at this time. 

Let's get started the show since the everyone sit.

Better say: Let's get started with the show now that everyone is seated.

The president called a meeting even in the early morning. --**Correct sentence~ ^^ 

This taxi driver always took on alternative route. --**Correct sentence~ ^^ 

We didn't still pick a date even though we need to book a flight.

Better say: We didn't choose a date even though we needed to book a flight.

I have a dental appointment this coming Saturday. --**Correct sentence~ ^^