Answers in your numbered order:
1) No./Yes./No. ... you had three questions buried in there. They first one is key; answer is No.

2) Yes./No (unchanged order). Again ... two questions ... and it's basically "good news".
3) Would be an issue ...
There is HOWEVER one possible situation your questions missed. Question 1b answer is YES. But there is a possibility that moving from old to new H/W that re-numbering could also occur. There's no way of knowing until you try. It could be chipset dependent, or even BIOS setting dependent (on the new hardware), especially because some BIOSes have "enhanced/legacy/combined/etc" options when it comes to emulating SATA/IDE combination motherboards.
Your question 3 seems to only deal with the situation once you are moved to the new hardware. In that situation the renumbering is very likely to happen. And unfortunately that could become a pain. ALSO NOTE: If you don't already have a backup of the failing drive (under question 2) it may be too late to "
simply back up that drive to somewhere else".
Suggestion: BEFORE you move any of the drives, try booting the existing USB stick on the new hardware (no drives attached) and make sure there are no other unanticipated issues (like the NIC not getting recognized) ... then move the SATA and PATA cards with a drive attached (they should work -- but better to try first (new IRQ issues ... etc) ) ... then move the rest of the drives.