Thus website says if your chimney us 2 bricks thick and that if the joints are staggered you don't need a liner. Is this not correct anymore?
http://inspectapedia.com/chimneys/Un-Lined_Chimney_Flues.htm
From that page I also saw residential building code requiring lining. This is a must. Lining will not only improve stove performance, it is a major safety improvement as well. A wood stove can and will get the flue very hot. Brick, even double brick, will transmit that heat to surrounding combustibles. And brick mortar will degrade over time, increasing risk. A proper insulated liner eliminates the worry and risk. This is really important if and when something goes wrong, and it will. For example, we get regular reports here of folks forgetting to close down the air on the stove. The flue in this case may see a sustained high temp of 1200F or higher for an hour or more. Yes, a liner is an additional expense, but consider it an investment. When something goes wrong, as it most likely will at some time, you will be thanking yourself for making this investment.
Note, the chimney must be thoroughly cleaned before lining. If you hire a certified sweep that person is qualified to do the lining. For a list of certified sweeps in your area enter your zip code in one of these sites:
www.csia.org
www.ncsg.org
To answer the wall thimble question, there is supposed to be brick 12" all around the thimble as it passes through the wall unless there is a special shielding thimble. This article covers the topic:
https://www.hearth.com/econtent/index.php/articles/passing_a_chimney
RR1001.8 Flue lining (material).
Masonry chimneys shall be lined. The lining material shall be appropriate for the type of appliance connected, according to the terms of the appliance listing and manufacturer's instructions.
RR1001.8.1 Residential-type appliances (general).
Flue lining systems shall comply with one of the following:
1. Clay flue lining complying with the requirements of ASTM C 315 or equivalent.
2. Listed chimney lining systems complying with UL 1777.
3. Factory-built chimneys or chimney units listed for installation within masonry chimneys.
4. Other materials that will resist, without cracking, softening or corrosion, flue gases and condensate at temperatures up to 1,800F (982C).