TIER 2 ICT: Is 28 days grace period after expiry applicable

[hnihalan]

I am in the UK on a Tier 2 ICT (Established staff) visa granted under the rules in place before 6th April 2011 and extend in May 2012 (as T2 ICT Long Term Leave to Remain) for another year. My current T2 visa is due to expire on 18 May 2013.
I have received an offer of employment with another employer, which is a Tier 2 sponsor with Unrestricted COS, and I wish to switch into the Tier 2 General. The sponsor is in the process of conducting the RLMT and the final day of advertising will be 19th May 2013 (counting 28 days of RLMT). However, my visa expires on 18th May 2013
I have a few concerns mentioned below
1) Can I still apply for my VISA on 19-may-2013 while I for am in UK? Is the 28 days relaxation post VISA expiry applicable to me? Also, will this create any issues for my current employer and there sponsorship license status?
2) If yes should I use the same day premium VISA application on 19th/20th of May? In case of rejection, will I have the right to appeal?
3) In case of rejection, can I apply for the visa from India immediately after my return to India or does a 12 month cool off period apply to me before I can apply
I will be really grateful for any guidance. Also are the guidelines on the 28 day grace period on the UKBA website.