Range on RFID is only 12 inches or so, did you know that?
There are lots of different kinds of RFID with a huge variety of ranges.
RFID is used for toll roads with the tag on the car's windscreen and the reader on a structure spanning the road.
RFID is used for 10K runs with the tag on the runner's bib and the reader on either side of the finish line.
Of course these aren't the sort of RFID tags and readers commonly used with the Arduino and I think your estimate of 12 inches is much too generous for most RFID readers and tags.
I've used the inexpensive MIFARE tags and readers (you can get a reader with a few tags for less than $3) with a couple different microcontrollers including the Arduino and the tag almost needs to be in contact with the reader. Maybe the reader can be 3" from the tag but I'd be surprised if the inexpensive readers worked at more than an inch of range.
There's a video showing the range of some of SparkFun's readers on this page.
The reading on that page costs more than 10 times as much as the ebay module I linked to earlier.
I think it's safe to say the inexpensive passive RFID readers/tags are very short range.
Not all RFID are passive. If you willing to put a battery in your tag you can have much better range.
OpenBeacon uses the inexpensive nRF24L01+ transceivers as part of their RFID tags. I've played with nRF24L01+ transceivers but I haven't tried using them as part of an RFID tag. Using nRF24L01+ transceivers in RFID tags is something I'd really like to try sometime. I think the transceivers are really cool little devices. They're really fast and really inexpensive.
Also it will only detect one object in the field,if there are two or more it doesn't work.
This isn't my experience. If I placed two RFID cards on top of each other and held them next to the reader, I'm pretty sure the cheap reader I used could read one of two cards. It wasn't necessarily the card closest to the reader. I'm not absolutely sure i'm remembering these details correctly but I remember being surprised the reader could read cards which were right next to other cards. I would have thought the coils would have interfered with one another.
The cheap readers don't have much range but IMO, they're really cool.
You will not get 60' from an IR sensor, more like 10' tops.
Here again I think there's a wide range of performance.
I think 10' is a bit of a low estimate of how far normal IR LEDs will be detected by an appropriate sensor but even if a normal IR LED is limited to 10' one doesn't have to use a normal IR LED.
As with visible light LEDs, there are lots of different IR LEDs. Adafruit sells these 100mA high power IR LEDs.
I wouldn't be surprised if the high power IR LEDs could be detected at ranges of 60'.
I noticed there's a requirement for video display. Video can be a problem for a lot of microcontrollers. It would probably be a lot easier to use some sort of LCD or OLED display. I like the OLED displays like the one I used in this video. The little 0.96" 128 x 64 OLED costs $5. This sort of monochrome display uses a lot less memory than than a VGA or NTSC display. The display buffer still needs to be 1024 bytes and if you want to do the graphic tricks seen in the video, you'll need twice that.
I don't have a whole lot of experience with the Arduino but I think most of the requirements shouldn't be a problem for most Arduino boards but the video and audio requirements my be too much of some boards. I'd think one of the Arm based Arduinos would have a better chance or meeting all your requirements. Something like the Teesy might be a better option.
I'm personally a big fan of the Propeller microcontroller which has eight 80MHz processors. The Propeller can output VGA and NTSC video but video is a memory hug and a single Propeller might not be able to meet all your requirements if you need memory intense video. When I need video in a project, I often "cheat" and use a second Propeller as a graphics slave.
A single board computer like the Raspberry Pi shouldn't have trouble meeting your requirements.