How to make team members more involved in the product, and keep the
development process smooth?
Have informal discussions with the team. Take them out for a beer or coffee and talk about what they think of the product or the latest/upcoming feature. Discourage technical discussions and if possible share the vision of the product and rough statistics of value(monetary or otherwise) it is generating.
People tend to see themselves as coders, managers or designers. They need to be exposed to the idea that they together are building something that has value in the real world. There is an owner, yes, but they too own the product in some way. There is more to it than just completing a task.
It is a mindset change and may take time to come by. Constantly pushing them to be more vocal will not help even if you continue doing it till eternity. Initially team members may also be repulsive of the idea about talking things they don't really need to know and find these discussions time-wasting. Hence, it is SM's task to make these meetings interactive and relaxing.
I normally tend to take the team by surprise shouting for an hour off and going out to parks, coffee places or bean bag room. There we just chitter chatter about the product. It is an unsaid understanding that whatever we talk, remains with us as a team talk. Nothing goes out to the management or anywhere.
What this exercise does is, it makes team members more aware of the product(than just code), they develop a sense of attachment to what they are building and that they understand they are playing an important role in increasing the statistics(business).
I have followed this experiment in my last three consecutive projects over period of 2 years. It works!
How to determine the priority of the ticket in a way that the team is
Once the team is involved in the project, it will happen automatically. Just ensure to listen to everyone and give them a convincing reason for every 'no'.
Can any team member create a ticket? How to determine if the ticket
has business value?
Yes. Let them create a ticket in the backlog. Discuss the feasibility of the ticket with the PO. If PO doesn't see any business value and wants to close the ticket, he should do so with a comment elaborating the reason for not considering the suggestion.
If team wants to create tickets, it is an indication that they are involving themselves beyond their primary task. They may not be as exposed to the market as business team, neither they may be business smart but the gesture deserves respect if nothing else.