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What are the upper and lower limits on Bitcoin Lightning channel balances and transactions, and where are these limits defined?

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Stuff like this can usually be found in the lightning-rfc aka BOLT (basics of lightning technologies) which is the formal protocol specification.

Currently channel capacity can't succeed 1/6 of a Bitcoin. However for BOLT1.1 (the next version of the protocol) it was agreed that this limit should be dropped (if both nodes of a channel agree to do so). Single payments should be less than 0.04 BTC. I don't remember if this is also supposed to be changed or even part of the Bolts or if it is just a self imposed limit by the implementations.

Balances can be up to the channel capacity. They are encoded in the commitment transactions which spend the funding transactions. So this part is defined by the bitcoin consensus rules.

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