1. of course!
any of the HDMI inputs can be used but look at your rear panel and find one that is labeled "BD". Use that one
but you can use any of them.
in that generation of Pioneer models, all the HDMI inputs except the named one "BD" (HDMI 1,2,3...) are unassigned to the named inputs (DVD, TV, etc). You can leave them that way (gaining more inputs) or you can assign them in your Input Setup menu so an HDMI input is bundled with the analog/digital named inputs.
read pg 48-49 in your manual, assigning inputs is described there. look at the chart on pg 49 which shows what inputs can be assigned or paired with HDMI, digital & analog.
and look at the rear panel diagram on pg 20.
2. in that generation of models, the Video Processor/Converter cannot be used with any HDMI input, hence "unavailable". it's not in the HDMI circuit path. Pioneer's design philosophy was that it was better to have the player or display do all scaling, processing, adjustments. keep in mind, they were making hi-end plasmas then (the best) and didn't want any processor in between to potentially degrade video quality, especially in uninformed hands, which I have personally seen in this forum from "know-it-alls" recommending their own personal settings to other uninformed owners and have those folks experience problems from double-scaling or poorer results. why would someone mess up an ISF calibrated TV by jacking around with settings that they may not know much about?
but starting with the SC-37, Pioneer changed its philosophy due to market pressure and allowed the Video Processor/Converter to be used on HDMI inputs. it's OK to have it there & have it be On, just be aware of what it does and what the settings are for.
but in the SC-27, you don't have the option to use it with HDMI anyway so moot point. if you want to do an occasional touch-up for a particular disc, you can do that in the player's settings. same for scaling content to 1080i/p. use the player's processor or the TV's. for the SC-27/25 models, the processor is for analog component, composite, & S-Video.
there you go