1: Use a Platinum rated PSU like the AXi 760w.
2: Those chips (first two) are dual core and BGA meaning soldered to the board. The following chips are also dual core but 1150 package and generally those are reserved for OEMs. For the money the i3 is also a 35w chip with HT so you get 2 cores and 4 threads still and available on Newegg. The other i5s you would probably need to check Ebay then find a board that supports them.
epends on exactly what you want to use this for. My initial answer will be probably not.
4:Full tower case, PSU outlined previously, any mATX or ATX board with at least 2 PCI-E 16x slots for RAID card. The card is to give you the max amount of ports and compatibility that you want without being limited to the motherbaord and 3rd party controllers.
5:Team Viewer or Windows RDT.
6:I was going to suggest this which highly depends on the application. If you are doing heavy HDD loads for whatever then internal would be best. Otherwise you could have endless amounts of storage using something like these.
Mediasonic HFR2-SU3S2 RAID 0 / 1 / 3 / 5 / 10 4 3.5" Drive Bays USB 3.0 & eSATA PRORAID Box 4 Bay Raid Enclosure with USB 3.0 & eSATA - Newegg.com
There are also 5.25" Drive bay modules you can use as well. So you could get a full tower and load it up with HDDs, then add basically HDD extensions.
7: TDP isn't amount of wattage used while under load. The i3 more than likely will consume slightly more power while the low wattage i5 is tailored for low wattage applications. The i3 will be faster though. Here again it highly depends on what exactly you aim to use this build for.
Edit: Answered questions in previous post. IMO just get yourself a NAS. For the amount of money you're looking at dropping here you could get a 5-8bay NAS which in itself will consume way less power than a standard PC and be tailored for exactly what you want software wise.