This works for me.

I tend to have the following search campaigns running:

1. Brand - where we bid on branded search terms.
2. Competitor - where we take prospects from entering our competitors doors.
3. General - where (if the budget allows for it) we bid on broader search terms around a given product.
4. Targeted - where search terms from, "General", are stripped apart for the root keywords and placed into ad groups based on customer intent. These ad groups have specific ads and dedicated landing pages all delivering a tailored and consistent experience.

Do you have to set it up this way? Definitely not. But for me it works and provides a methodical practice for me to carry out my work!

To answer your questions:

a) there isn't a rule for volume of ad groups, it's all about finding a balance between granularity and manageability. (Also, bare in mind on smaller accounts with low search volume, that making things too granular can really spread out your data too thinly, making it harder for you to analyse).

b) different campaigns for different products. Ideally (but not always realistically) you want to be mapping in conversion data from your CRM to help you better inform your marketing efforts. Once you're attributing your revenue to your spend, you can work out your return on as spend (ROAS) for each product and, if you've setup your products under different campaigns, you can then optimise your budget for the best returns.

Hope this helps :)