Tier 2 change of employment

[priyabiradar]

Hi,

My visa is due to expire on 29th of march 2017 and my application for extension is ready to apply online but I have got an offer from new company who is ready to sponsor tier 2.
They are planning to generate new CoS by 14th of march and want to make an online application for me and my dependant on 17th of march. Also planning to book priority visa appointment in 1st week of April depending on availability .
In my case when do i have to handover notice to my current employer? My notice period is 1 month.

If i handover notice after 17th march then my current employer may only allow me to work until 29th march as they are sponsoring me until 29th. so I may lose my more than half of my salary as i failed to handover 1 month notice. Is it true that i may not legally work for my current employer whilst I'm waiting to get decision on my visa extension with new employer after my previous visa expiry?

If i handover notice now immediately and serve 1 month notice period than i may have to stay at home without work in April until i get my new BRP. Does this waiting period may effect my ILR in future ? Also if for some reason my visa gets rejected and new employer denies to assist further with my visa application then i would have to return back to my county.

Is it wise to make an extension application now with current employer just by myself without dependant using premium service and re-apply again with new employer on 17th march along with dependants to play safe? Please suggest me best option.

Also how about my dependant? can they continue to work whilst waiting to get decision on our visa extension.?

Much appreciate your help.