There's no reason at all why you can't all have access to the passwords. The NALC (National) site is full of useful information for councillors, especially those new to the role. Your local ALC will provide a reange of training and support services which you will find useful from time to time. I probably shouldn't say this on here, but the NALC password will be the same one your neighbouring parish councils use, so if you have a word with somebody there, they might be able to help you. NALC forbid the sharing of passwords with councils that haven't paid their subscriptions, for obvious reasons, but if your council is a paying member, it isn't an issue.
And yes, you can record the meetings. The rules permit anybody to record for any purpose.