Unfinished Tier 5 to Tier 2 Advice needed urgently!!!

Hi All,
I am on a Tier5 (Government Authourised Exchange) Visa. I have been in the UK in a scheme that should last for 1 to 2 years. Its my 10 month already and I am not keen on continuing. I recently applied for a better job and after the RLMT was applied I got offered. The new job offers more money and the work permit (Tier2) counts towards ILR. I am aware that switching to Tier 2 has to be done out-of-country. I do not want to lose my Tier5 and then get rejected when applying for Tier 2 from my home county. My prospective employers have agreed to get me a CoS if I accept the offer.

Questions

1. Is it mandatory to complete ones Tier 5 to be eligible to apply for Tier 2? I am worried that my Tier5 sponsors may mention to UKBA that I left prematurely.

2. Is there a cooling off period when switching from my type of Tier5 to Tier2. I don't want to be told that I am not eligible to return to UK for the next 12 months or so when I am in my home country.

3. I applied for the new job whilst in the UK on Tier 5. Is that wrong? Am I expected to have relinquished my Tier 5 before applying for Tier 2?
Am I expected to apply for the job (not the visa) from my country?

Bottomline there's a saying "a bird in hand is worth 2 in the bush"

But the bird in the bush is really big and enticing!

Questions

1. Is it mandatory to complete ones Tier 5 to be eligible to apply for Tier 2? I am worried that my Tier5 sponsors may mention to UKBA that I left prematurely. No

2. Is there a cooling off period when switching from my type of Tier5 to Tier2. I don't want to be told that I am not eligible to return to UK for the next 12 months or so when I am in my home country. No

3. I applied for the new job whilst in the UK on Tier 5. Is that wrong? Am I expected to have relinquished my Tier 5 before applying for Tier 2? Two things, you can not switch from Tier5 to Tier 2 in country and your Sponsor should have applied for a Restricted COS
Am I expected to apply for the job (not the visa) from my country? see above

Hi Frontier,
I am so grateful!
My Tier 5 is due for extension by 31 August. I have an exam from 6-9 of September in UK. I plan to leave on the 10th of September to go apply for my Tier 2 from my home country. Would the period after August be classed as illegal stay?
Thanks

You have a 28 day grace period to leave the UK without it counting against future visa applications.
Is your current sponsor intending to sponsor you further for Tier 5 purposes?

Yes, my current sponsor are happy to extend my Tier 5.
But i want to rather take the Tier 2 job offer. Counts towards permanent residency and better pay.

The only reason I asked was to see if you can extend on Tier 5 thus avoiding any period of overstaying even just in the grace period.

Can you take your exams on your return rather than overstay?

Thanks.
Yes the process of extending a Tier 5 and then changing to Tier 2 is costly and would involve signing a contract, and my resignation would be subject to a 3 months notice. I will call UKVI today to clarify.