ILR - 10 year LR - break between visas

Dear all,

I arrived UK on 19/09/2009, and plan to apply for IRL within 28 days of 19/09/2019 (say 26/08/2019).
I did stay in the UK legally the whole time. However, I have a big break between my Tier 4 and Tier 2 visa.

End of Tier 4 visa, left UK on 31/05/2017
Submit for Tier 2 visa on 28/08/2017 (89 days since I left UK)
Arrive UK with Tier 2 visa on 18/09/2017 (110 days since I left UK)

1. Does this 110-day gap break continuity?
2. By the way, do we plus 1 to day difference, e.g does "leave UK 20/12 then enter UK 22/12" count as 2 days or 3 days absence?

Thanks for your time

1. Does this 110-day gap break continuity?

If on the day you left the UK, you had valid visa then you should be fine as you returned within 6 months.

2. By the way, do we plus 1 to day difference, e.g does "leave UK 20/12 then enter UK 22/12" count as 2 days or 3 days absence?

The days of departure and arrival do not count. Only full days count as absences