New member here, both Liverpool and Red Star Fan. Don't live in Serbia anymore but try to keep up as on whats happening there, so wanted to give you some advice before you travel.
Don't take this as an official advice, I can only state what was happening historically, this is new realm for Red Star to be in Champions League.
1. As far as I know there is no bad blood between Red Star Fans and Liverpool. There are countless Red Star fans that truly love Liverpool. (Me being one of them)
2. As far as the crowd troubles go its still there but to much lesser extent, especially at the stadium. I can not remember last time there was an incident in European Match that involved massive fights and troubles. Most of the fines that Red Star incurs is because of the Political Messages that fans have towards the UEFA and World.
Historically you will be placed in a box. usually they reserve between 5-10k spots for visiting team. you will be very well protected there, if there is any sign that visiting fans might be in trouble, there is plenty of Police reinforcement on the standby around stadium, and they will be there before someone can even breach the first perimeter of security (this is more for teams that fans have bad blood against). Police takes security of the visiting fans very seriously. They will place you on the southern sides to move you away from the North where the Ultras are. Now as far as the East and West goes, you'll probably be fine even in Liverpool Jersey (There are always idiots that just want trouble, can't speak for those), but honestly I would stay away from the North, they expect you to cheer, stand, and sing through the whole game, and there are known incidents where even Red Star fans got in trouble on North because they didn't sign, or they sat down, etc... Just as a precaution stay away from North, you never know who you might run into. It's not England, laws are not there yet for the North Side.
As you arrive in Belgrade, stay in Groups, avoid secluded areas while wearing Liverpool colors. Again my understanding is that Red Star fans have no bad blood and will not look for fights with you, but as a precaution stay in tourist places. There will be plenty of police on the game day to keep an eye on situation.
As far as the ticket prices go, the price listed here was for the set of 3 (All 3 games in GS). Not sure what they'll charge you guys.