Brick Chimney To Wooden Chase Questions

The top 3rd of my chimney (mostly above roof line) has bad spalling and needs repaired. I can do about any type of work but have never done masonry work. I am considering transitioning to a wood frame chase at the roof line. Here are some of my concerns as I plan the job.

1- The top two clay flue liners will be replaced. Is there an adhesive product I can use between the old existing liner and the new one, or must I use a refractory mix?

2- Can the new flue liners rise up through the wood chimney chase with no horizontal support, as opposed to having rubble-fill like in a brick chase? The top crown will be much lighter than concrete.

3- How much clearance should there be between the flue liner and the chase walls?


Thanks in advance for comments and any suggestions.