Tier 4 to Tier 2 Employer sponsored,Start date so long time

[Kota]

Hi Dear,
I graduated on 13th Feb,and my current Tier 4 is due on 15th May,However i got job and employer is ready to sponsor me but the job starting date is from 10th July.I will switch to Tier 2 in country on may,
1)How many days do T2 will be active based on my job start date or CoS start date(let say CoS start date is 1st july) ?
2)Let say T2 will be starting from 20th June,do i have to go back my home country and enter UK only after 20th June ?
3)Or does UKBA will give Visa from 16th May(immediate date after my current visa expiration date) ?

Thanks in advance