-I see that bech32 addresses have bc1 at the beginning, is this the part that will always repeat to recognize the segwit transactions?
Yes. That is the human readable part of bech32 and will be the same for all bech32 addresses. Bech32 addresses are different from the legacy addresses (1.. and 3..) since it uses a different encoding.
-I also noticed that there isn't a single character with capital letters. How come there are no caps at all? Im used the classic format and seeing it all in small characters is pretty weird. Im not even sure of legacy format being caps sensitive, but I think it was easier to recognize the shape of the address if there are caps on and off or maybe that is how my brain works.
Bech32 uses a different encoding scheme which is case insensitive unlike the legacy address scheme which is case sensitive. Legacy addresses are encoded with base 58. However bech32 encodes things with base 32 which does not include any casing.
About caps sensitive.. what would happen if instead of 12sziC91z7hwfpVDNw7UbsisaapBwFtW7t you send BTC to 12szic91z7hwfpvdnw7ubsisaapbwftw7t ?
The address should be invalid. It is case sensitive, so that would be wrong.
-In the case of a split into a fork of BTC that doesn't support the segwit format... how would you receive your share?
For example if the BCH fork happened after segwit got activated and you were holding 1 BTC in address bc1qzjw3jywhf2r7k24y3gqj0fs4apddg03pujsjzx, how are you supposed to receive your 1 BCH on the other chain?
Since segwit has already activated, such a fork would result in you losing any and all money that is in a segwit output, both nested and native. This is because such a fork without segwit would regard all of those outputs as anyone-can-spend outputs and the miners who initiated that fork would steal all coins in segwit outputs and send them to themselves.
To actually spend those, for native outputs, you would just have an empty scriptSig and it would work. For P2SH nested ones, you would just put the redeemscript in the scriptSig and it would work. There would be no place for signatures to go.