Jonathan,
There is nothing special about a UV-5RA. The extra 'A' tacked on the end (as well as the plus and all other letters that you see appended to UV-5R) only indicates a particular case style. The electronics inside is basically the same. The real variation is in the firmware versions. CHIRP works with all 144/440 UV-5R models and all firmware versions that I know about.
1) Does the backlight not come on at all? The UV-5R has a quirk (the UV-5R has lots of quirks) that if the backlight is off and you press the PTT button or a signal is received, the back light does not come on. Then after you release the PTT button or the received signal goes away, the standby backlight will come on. Then if you press the PTT button or a signal is received before the Standby backlight goes out, the TX backlight or RX backlight will come on. The backlight will continue to work properly until the standby backlight times out. This is not a CHIRP issue.
2) How do you mean the tones and offsets are not registering? I loaded your image file into CHIRP and all looks as it should. I then uploaded it to my UV-5R and all works as it should. All of the CTCSS tones and DCS codes are there as expected and the repeater channels appear to be working.
Menu 25 (SFT-D) and menu 26 (OFFSET) are not valid in channel (memory) mode. This is because the UV-5R does not use them at all when storing memory channels. Memory channels store the RX frequency and the TX frequency. Even though the CHIRP UI lets you enter them as a RX frequency, shift direction (Duplex) and Offset, CHIRP uses these values to calculate the TX frequency so it can send the UV-5R what it uses.
Tune in a repeater channel. If the display is set to show FREQuency, then you should see the RX frequency. The upper status display should have a "+-" indicator showing (not a "+" or "-" by itself). A "+-" indicates that the RX frequency is different than the TX frequency. You will get this same indication if the channel has TX inhibited. Tap the [*SCAN] key to activate Reverse Mode. The TX frequency should now be displayed. Tap the [*SCAN] key to exit Reverse Mode.
Visit the Miklor website and look for MENU DETAILED REFERENCE on the home page for links to the Reference for UV-5R Menus. It show which menus are invalid in memory (channel) mode and which menus are Read Only in channel mode (like the CTCSS and DCS menus).
http://www.miklor.com/uv5r/
3) Programming manually can give you a better understanding how the UV-5R works. The biggest issue with new UV-5R owners is that the UV-5R works differently that what the user expects.
I don't think there is a CHIRP issue here. Please review the menu reference to gain some understanding of how the radio works then try CHIRP again. If there is truly an issue with CHIRP, we definitely want to help you with it.
Jim KC9HI