Tier 2 General change of employment within UK

Hi All,

I have 2 queries about change of employment in UK.

I am an Indian national currently working in UK on Tier 2 General Visa valid till March 2016.

1st Question
My current employer has asked me to work from India for different assignment starting from 1st October 2014. Therefore I wish to resign from my current company and look for a job in UK.

Can I do that? If so, how many days am I allowed to stay in UK and find a sponsor?

2nd Question
I am expecting an offer from a company in UK that is willing to issue me a Certificate of Sponsorship after it has successfully completed RLMT, which will complete on 15th October.
If I dont resign and work for my current employer from India while my visa is still active, can I come to UK for applying new visa after the new prospective employer has issued me a COS? (On 16th October)

Looking for an early reply. Thanks a lot in advance.