Lots of confusion here.
There are 4 generations:
SD(SC)The original standard, retrospectively named "standard capacity". Card capacity up to 4GB can be encoded and the officially supported filesystem is FAT16. Some implementations of FAT16 may not understand 64KB clusters and therefore 4GB FAT16 volumes. The same devices may or may not support FAT32 - this was never required by SD, but could be part of the embedded OS they use.
The subsequent SDHC standard forbade 4GB capacity cards and required them to be SDHC instead, but rare 4GB SDSC cards exist.
SDHCA new standard introduced in 2006 and implemented by most devices since then. The Card Specific Data register layout has been modified to encode large capacities (but only 32GB is permitted by the standard) and version number increased. Pre-2006 devices refuse to read such cards and if they attempted anyway, they would decode the capacity completely wrong. New commands have been added too and SDHC hosts issue at least some of them to all cards but SDSC cards reject them. The official filesystem is FAT32 but many devices will work with FAT16 on a sufficiently small partition.
Rare 4GB cards exist that are dual-mode. They watch the commands issued by the host and present a 4GB SDSC CSD to SDSC hosts and a 4GB SDHC CSD to SDHC hosts.
Because SDHC forbids 4GB SDSC cards, some pedantic SDHC hosts may reject a 4GB SDSC card. I think I have owned one such device, but I sold it so can't confirm.
Because SDHC forbids 64GB+ cards, some pedantic SDHC hosts could reject SDXC cards.
SDXCIntroduced in 2009, mostly same thing as SDHC, but cards 64GB+ are permitted and mandated to use exFAT.
Some SDXC hosts (Panasonic, I'm looking at you) actually enforce this and refuse to read FAT32 formatted SDXC cards, others don't give a damn.
FAT32 formatted SDXC cards generally work in SDHC hosts, but I have encountered issues with excessive memory use on such filesystems. It helped to increase cluster size, thus reducing cluster count.
SDUCSome 2018 thing I'm not familiar with.
Then there is a completely orthogonal issue of interface speeds which have been added over the time. AFAIK, all cards and hosts support some lowest common denominator SDSC speeds and can figure out the highest speed supported by both peers. Never had problems with that.
Using a 2GB partition can only solve filesystem compatibility problems - presumably lack of FAT32 support. It will not enable a pre-2006 device to work with SDHC or SDXC.
Question 1:
My understanding is that the MicroSD to StandardSD adapter is purely electrical, MicroSD pins to Standard SD pins in the adapter and therefore "size insensitive". The adapter that that works for 32gb should work just fine for 64gb. Am I correct?
Question 2:
Since the CHS limit is around 8gb, these card readers are using LBA. I know there is an LBA limit around 128gb. Am I safe to assume that "high probability" the 32gb card readers should work fine with 64gb SD?
Adapters are dumb and SD cards have their own sector addressing schemes which differ between SDSC/SDHC. CHS/LBA only comes to play when an SD card is used to emulate a magnetic disk, for example by plugging it into a USB Mass Storage type reader. Problems are unlikely to arise in practice because software that supports USB tends to support LBA too. I imagine there could be issues if you attempt to boot DOS from such card reader.
USB SD card readers come in two flavors. Some are pure SD hosts and the software needs to know how to talk SD and tell the card reader what commands to issue to the card. Others handle SD internally and appear as generic USB Mass Storage devices.
The former type will work with every card, the latter will not work with SDHC/SDXC if it was made before 2006. In principle, SDHC readers ought to work with SDXC because the difference is filesystem (handled by the OS) and an artificial capacity cap imposed by the earlier standard.