My understanding is that you can access money in your RRSP for a HPB withdrawal, as long as it is in the account for at least 90 days and not locked-in, and meets the other conditions. It doesn't matter that it was transferred from an RPP because you changed/lost a job.
As for the second question about reporting Lump Sum RPP to RRSP direct transfers, as far as I can tell, you are not supposed to report such a Transfer in Schedule 7. The CRA website states, "In most cases, if you transfer an RPP lump-sum amount directly to another RPP, SPP, RRSP, PRPP or to a RRIF, you do not have to include any part of the amount in your income, and you cannot deduct it. However, the Income Tax Act limits the amount you may transfer on a tax-deferred basis from a defined benefit provision of an RPP to a money purchase provision of an RPP, an RRSP, or a RRIF."
The majority of RPP funds paid entirely by the employer can only be transferred to locked-in accounts (LIRA or current employer's RPP). If you have contributed to the RPP directly, it may be eligible to be moved to an unlocked plan.
If the RPP funds you are transferring can be moved to an unlocked RRSP, there should be no problem with using the contribution for the HBP, assuming you meet all the other criteria. When you do the transfer to the new RRSP, confirm with the RRSP administrator that you're transferring to an unlocked option that's HBP eligible.
When the transfer is requested, you'll be given all the options available to you. Along with the list of options will be the amount of the RPP that is over the transfer limit (if any). These funds will be payable to you upon the transfer. Tax is usually withheld because this portion of your RPP is taxable. The funds that are actually transferred are not taxed (and do not need to be declared on your return) if the transfer is made directly to another plan.