1.)

Pi2B 4.4.38-v7+
dtparam=i2c_arm=on
-----------------------------------------
pi@raspberrypi:~ $ dmesg | grep -i i2c
[    2.608025] i2c /dev entries driver
[    3.658629] bcm2708_i2c 3f804000.i2c: BSC1 Controller at 0x3f804000 (irq 83) (baudrate 100000)


Pi2B 4.4.38-v7+
dtparam=i2c_arm=on,i2c_arm_baudrate=10000
-----------------------------------------
pi@raspberrypi:~ $ dmesg | grep -i i2c
[    2.598790] i2c /dev entries driver
[    3.579219] bcm2708_i2c 3f804000.i2c: BSC1 Controller at 0x3f804000 (irq 83) (baudrate 10000)


Pi2B 4.9.11-v7+
dtparam=i2c_arm=on
dtoverlay=i2c-bcm2708
-----------------------------------------
pi@raspberrypi:~ $ dmesg | grep -i i2c
[    2.623397] i2c /dev entries driver
[    3.515470] bcm2708_i2c 3f804000.i2c: BSC1 Controller at 0x3f804000 (irq 83) (baudrate 100000)
[    9.129662] i2c i2c-1: transfer timed out
[   12.409664] i2c i2c-1: transfer timed out
[   13.449661] i2c i2c-1: transfer timed out
[   14.489659] i2c i2c-1: transfer timed out


Pi2B 4.9.11-v7+
dtparam=i2c_arm=on,i2c_arm_baudrate=10000
dtoverlay=i2c-bcm2708
-----------------------------------------
pi@raspberrypi:~ $ dmesg | grep -i i2c
[    2.580957] i2c /dev entries driver
[    3.495826] bcm2708_i2c 3f804000.i2c: BSC1 Controller at 0x3f804000 (irq 83) (baudrate 10000)


2.)

Pi2B 4.4.38-v7+
---------------
pi@raspberrypi:~ $ ls /proc/device-tree
#address-cells  chosen      cpus              memory      name           #size-cells  system
aliases         clocks      interrupt-parent  memreserve  __overrides__  soc
axi             compatible  lirc_rpi          model       serial-number  __symbols__

I checked down through the entire device-tree directory tree and there is no sign of a hat directory anywhere.

I had been under the impression (based on statements from the developers, IIRC) that there is an EEPROM on the UPS PIco, but I don't really know.


3.)

Pi2B 4.4.38-v7+
---------------
pi@raspberrypi:~ $ cat /proc/cmdline
dma.dmachans=0x7f35 bcm2708_fb.fbwidth=1360 bcm2708_fb.fbheight=768 bcm2709.boardrev=0x3a41041 bcm2709.serial=0x626aa24a smsc95xx.macaddr=B8:27:EB:6A:A2:4A bcm2708_fb.fbswap=1 bcm2709.uart_clock=48000000 bcm2709.disk_led_gpio=47 bcm2709.disk_led_active_low=0 vc_mem.mem_base=0x3dc00000 vc_mem.mem_size=0x3f000000  dwc_otg.lpm_enable=0 console=tty1 console=ttyAMA0,115200 root=/dev/mmcblk0p2 rootfstype=ext4 elevator=deadline fsck.repair=yes rootwait quiet splash plymouth.ignore-serial-consoles