Speed negotiation is part of the SATA initialization protocol. Any controller worth it's weight properly implements this. Some early VIA and SiS chipsets were known to fail at this, but I would expect better from the SAS 5i/R (LSI, I believe?)
That's a lot to address. I'd keep the existing Smart Array p400 controller in place for now, provided it has a working battery-backed cache unit. Otherwise, your LSI will work, but it's not ideal.
The on-disk RAID formats are different, so this means a full rebuild. You won't be able to preserve your data if you do what you're proposing.
As for 3G versus 6G, it does not make a difference unless you're dealing with SAS expanders or solid-state drives. You won't see any difference in performance in your case.
I tend to think that HP controllers run better in their servers. I'm also not a fan of LSI's management software (MegaCLI is awful). Using LSI HBA cards for other solutions makes sense, though. Your best bet in this case is to make sure you have an HP P400 controller with BBWC cache (here's why). If you don't have the cache, your path of least resistance is to obtain one.
That way, you can be sure that your backplane, alerts, LED indicators and integration with system monitoring all work properly.
As for rails, check:
http://www.racksolutions.com/hp/racking-hp/ml350
Best Answer
Yup, here is the info I found: http://www.dell.com/downloads/global/products/pvaul/en/6gb-sas-transition.pdf
6Gb/s SAS is designed for backward compatibility with 3Gb/s SAS and 3Gb/s SATA
Here is anandtech testing a 6gb/s drive in both 6gb and 3gb controllers:
http://www.anandtech.com/show/2866/3 (sata, but should be the same)