Lateral entry

There is no difference between B.Tech and B.E. as both is engineering degree just a name difference.
MS Ramaiah offers B.E. not B.Tech but no problem its engineering degree.
Check College details in the link provided:
https://www.shiksha.com/college/m-s-ramaiah-institute-of-management-m-s-ramaiah-banga

Engineering Colleges/Universities offering LEET admissions are
* Punjab University - Chandigarh
* IP University - Delhi
* Delhi Engineering College - Delhi
* Punjab University - Patiala
* KIITS University
* Thapar Institute of Engineering and Technology - Patiala
* Government College of Engineering - Pune
*

DTU offers lateral entry and there are universities like Indraprastha University in Delhi NCR.

To get lateral entry in the B.Tech you need to clear your diploma of 3 years with at least 60% marks the colleges that offer lateral entry in the engineering are as follows:
Lovely Professional University-Jalandhar,
Adamas University-West Bengal,Techno India University-West Bengal,JIS University-Wes

You can't get admission in NIT through lateral entry because they take students only via JEE Mains.

Yes, if you have diploma in civil engineering you can surely get lateral entry in B.Tech architecture but some colleges has some colleges on their own rules. Most universities usually take the lateral entry for civil engineers to the B.Tech architecture you can surely search for that.

Yes, you can surely get the lateral entry to the second year of B.Tech if you have diploma in electronics engineering. There are various colleges which provide lateral entry to the diploma students.

Yes, you can do it, but in some colleges, there might be restrictions so I can suggest you a university where it would not be a problem, it would be LPU.

You can look for Vivekananda Institute of Technology-Jaipur, Lovely Professional University-Jalandhar, Adamas University-West Bengal and JS University-West Bengal. All these universities and institutes have scholarship scheme for its students.