Well, nobody seems interested so here's my 10cents.
1. No - but if you are looking to actually contact a particular receiver rather than just a random distance then HF power is more likely to make the contact rather than VHF. VHF works over long distances if you have a straight line between you and him - visual contact in fact. This is why you can hear aircraft on VHF for 300miles or more as long as they are at 25,000ft or more - and 25watts will do it just fine. But HF will run out long before that - the ground wave may not go more than 25miles before it fades out - and the first return of the sky wave may not come down until maybe 100miles - unless you make your antenna and the right frequency to make what they call NVIS - near vertical incident skywave - it goes up and it comes straight down. But then again there are "QRP" contacts - very low power, say 5 watts or less, and particular forms of modulation that will go around the world. So the short answer to your question is - maybe!
2. Yes - DC to daylight - and past daylight!
3. There are round-the-world communications on extremely low frequencies - see -
List of VLF-transmitters - Wikipedia - some of those transmissions are in 'Hertz' - but the reception is of very low signal strength so they have to resort to very complicated methods of digging the signal out of the mud - look up 'coherent detection'. Your GPS receiver uses these techniques - the signal is actually much lower than the noise - but the noise is random and the signal is not - so if you keep sampling time and time again you will find that the noise is not
re-occuring but the signal is, then you can cancel the noise and what is left is signal - but as you say the data rate is very slow.
4. A 1cm antenna will receiver signals best where 1cm is a quarter-wavelength - so the frequency will be 300/4cm - which if I have pressed the right buttons is about 12,000MHz - hardly HF. The best antennas are based on a quarter wavelength so if you want to receive, say 10MHz you need a quarter of 30metres, 7.5 metres, 25 feet.
5. None, but a simple dipole is about 2.1dB down on an isotropic radiator.
Now lets wait for the flame-throwers who have been lurking in the back room - just going to pounce.....