1. You have 10 days to register in CA.
But I don't think it is strictly enforced. When I brought my papers in to the DMV and they asked me when I brought the car into CA, I said 7 days ago.
2. It took them about 2 weeks (14 days) to send me the docs. I'm thinking if you really need them sooner you can ask them to make sure they expedite it to comply with CA laws. It wasn't a big deal for me.
3. they provide all the forms you'd need, except the smog certificate. The DMV form (forget what # it is called), the certificate of origin (like a title doc), the VIN verification form (although my DMV rejected it and asked me to do VIN verification there that same visit). A check made out from Heuberger to DMV for the sales tax costs (that they charged you already). You need to, in advance of the DMV visit if possible, take your car in to a smog place and get smogged. The test center will e-submit the cert to DMV but it's best to bring a hard copy of the pass results with you. The DMV form will be mostly filled out for you which makes it easy. I did finance through an outside lender not through the dealer, so I did have to fill out the section that indicates who the lien holder (the bank) is. I imagine if you financed through HB they will fill it out for you already.
4. HB charged me for sales tax but not for CA registration fees. So those are due at the time you register in CA. I paid about $288 or so at the DMV?
Reread the post of mine that you quoted - I think I actually answered most of these already back there.