Electronic – arduino – Simple solar panel + supercap powered arduino

Long version (full story, so skip and go direct to questions below if you want to):

I have small arduino mini pro board powered by 230mAh Lithium coin battery used as wireless sensor (with NRF24L01 and different sensors)
I use a 1.8V or 2.4V LDO regulator and modified bootloader (lower frequency = lower consumption). Periodically it take measurement, send it and go to sleep (Board modified to go down to nA consumption). This work well multiple months, I'm happy.

But I found a new greener challenge: Power it without battery only by ambiance luminosity. I want to use a 12V (1.5W max) solar panel (I hope to get at least 2.8V with artificial light, I will verify this by testing) combined with a supercap (10 Farad for example)

I found some examples with IC's to control voltage and limit current: Bicycle example
But I wonder if I could make it simpler directly with only a LDO regulator.

For a 10F supercap and an 2.5V (180mA max) LDO regulator I get:
Charging time = (2.5/0.180)*10 = about 2 minutes 32 seconds

Questions:

• Will my first 2.5V LDO regulator survive without current limitation, or do I need a mosfet like this : Instructable. I could add a resistor too, but that's energy wasted no?
• Do I need more schottky diode to prevent some current leakage?
• Can I use a 2.7V LDO regulator instead 2.5V one or It's better to stay a little away from supercap voltage limit even by loosing some power?
• (I will see if power consumption is better with second 1.8V LDO regulator and a lower working frequency or if it's totally useless against using only the first one)

(Sorry for my poor English)

Edit 17/09/2018:

By searching other regulators with current protection I wrote this small tab:

MCP1702 is a better choice cause of thermal protection? But expensive for a SOT23 package : 0€42/piece. LP2985AIM5X-2.5 seems to be at 0€18/piece. I don't find other with Vin >= 12V on aliexpress for 2.5V output (most are 3.3 or 5V).

Edit 17/09/2018-2:

I found this example but for now I doesn't understand it all.
After @HarrySvensson comment suggesting to use MPPT to get more efficiency, I wonder if using some MPPT board for charging Lipo Like this one and putting the LDO regulator after it could be a good idea or absolutely not? (I looked the CN3791 datasheet I don't find any way to adjust output voltage)

Edit 18/09/2018:

And what about This one? Voltage and intensity are apparently adjustable. But I'm not sure this is a real MPPT board, it seems more like a buck converter.