Re: landing on my back in forward roll
You might find it helpful to see your very first movement towards attacking nage as being the begining of your ukemi roll.
Although there will often be some time between this point and the momment that you actually start to tumble, you may feel safer (like when practising alone at the start of the class) in the knowledge that you have a degree of control in the process. You will hopefully begin to notice the direction that nage is leading you in more quickly and precisely, and therefore be able to guage for yourself when the best time to tumble is. As your confidence grows, I'm sure you will begin to notice more and more, the times that you are rolling too early, too late and just right. As well as having a bit of natural uncertainty about the physical aspects of falling, it sounds like you may be waiting to be thrown, which is leaving you with less time and fewer options as ukemi than you'd need to feel entirely confident.
All the best