Tier 2 General. 3rd time.

Hello everyone,

I would absolutely appreciate if anyone can help me with understanding of the options I have in the next situation:

1. Got Tier 2 General visa in February 2014 from outside of the UK and worked for 2 years for my sponsor. My wife accompanied me and got Tier 2 Dependant visa.
2. I decided to switch my job and found another sponsor in the end of 2015. I got a new Tier 2 visa (leave to remain) in February 2016. My wife got another Tier 2 Dependant visa with me.
3. In February 2016 (first day of my new job) it was announced that my new company is going to be closed by its owner on April 15th 2016 and my visa goes to hell with it.
4. My last company decided that it is ok to get me back and they are willing to sponsor my new (3rd one) Tier 2 visa. Currently they are placing a job advertisement and applying for CoS and I am waiting for 4 weeks and then can apply for another Tier 2.

I have a couple of questions about this whole situation and things I need to do to apply the 3rd time:
1. I have been told that I would need to submit a verified copy of my diploma from a university I attended. I did not need to do it last time I applied (February 5th 2016). Were there any changes to the process in the last month?
2. I would need to pass an English test. I passed IELTS when I was applying for my first Tier 2 from outside of the UK.
I did not pass any English tests last time I applied (February 5th 2016). Same question - were there any changes to the process in the last month?
3. Is there any cooling off period if I apply for the 3rd time? Any cooling off period for my wife (Tier 2 Dependant)?
4. Am I right that I can legally stay in the country until my current employer shuts down and I receive a curtailment from the Home Office?

Many Thanks!