Regarding question 1:
There are currently very few mainboards or none that have a TPM 2.0 module permanently installed. This refers to mainboards for self-build PCs. However, some offer the option of buying a TPM 2.0 module as a separate module and retrofitting it on the board in a slot provided for this purpose (
https://de.wikipedia.org/wiki...).
In addition to physical TPM modules, there are also fTPM (firmware TPM, called PTT at Intel).
Intel and AMD have been integrating TPM version 2.0 into their CPUs for several years. To be able to use this, the BIOS of the PC/notebook must support it and it must be activated there.
Intel CPUs from the 8th generation onwards usually have TPM integrated. Intel calls this PTT (Platform Trust Technology). AMD has integrated TPM as fTPM in the CPUs since the use of Socket AM4 from around 2016.
List of Intel CPUs that officially support Windows 11
https://docs.microsoft.com/en-us...
List of AMD CPUs that officially support Windows 11
https://docs.microsoft.com/en-us...
FAQ about TPM 2.0
https://www.heise.de/select...
Before buying a TPM module for the mainboard, which may be unnecessary, you should check whether the possibility of fTPM / PTT via CPU is possible in the BIOS and whether this only needs to be activated.
Help pages for (f)TPM from various mainboard manufacturers:
ASUS
https://www.asus.com/ch-de...
MSI
https://www.msi.com/blog...
Gigabyte
https://www.gigabyte.com/Press...
Asrock
https://www.asrock.com/support...
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Regarding question 2:
https://rog.asus.com/ch-de...
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Re question 3:
Boards with B550 chipset have no fans and are not that much worse. There is a new version of the X570 (X570S) that does not have a fan, but these boards are only just coming onto the market. But the fan has never been a big issue so far, it's always quieter without one.
https://www.computerbase.de/2021-05...
To your last sentence. There is no combination of no chipset fan and TPM, as there are no boards with TPM. At least I haven't found one yet.