Even if the actor who played Finn had died recently and it is not going to work finding a new actor/singer to play Finn at all, then did I read that some TV critics think that the Finn character is too problematic to resume?

They're not going to replace Cory. The 3rd episode of the upcoming season will be a tribute to him.

Get ready for tomorrow night.

After that, Rachel will concentrate on Broadway for the rest of this season, but by the end of this season she will find a a brand new boyfriend with these important requirements:

- A broadway type.

- An experienced singer and actor.

- No erratic love techniques.

- No drug dealings.

- No alcohol substances.

- No rudenesses.

Do I make myself clear?

Get ready for tomorrow night.

After that, Rachel will concentrate on Broadway for the rest of this season, but by the end of this season she will find a a brand new boyfriend with these important requirements:

- A broadway type.

- An experienced singer and actor.

- No erratic love techniques.

- No drug dealings.

- No alcohol substances.

- No rudenesses.

Do I make myself clear?

I read that Rachel's character will not move on from Finn this season, and I hope that is true

Not for long. She will remember Finn as a high school sweetheart, but she will find a new boyfriend during her broadway level.