Distance/Correspondence B.Arch

Doing B.E. / B.Tech/ B.Arch through distance mode is not valid as per UGC guidelines. So never be pursue. B.Arch through regular mode is the best option. Further both courses also can not be pursue simultaneously through regular mode.

No, no such institution or university exists where you can get a B.Arch through distance education. Regards.

No, you can check the website of IIA. The Indian Institute of Architects run its professional associateship examination equivalent to B.Arch and the recognition of the examination is also required to be checked by you before taking the admission. The Indian Institute of Architects (IIA): https://indianinstituteofarchitects.com/

Pleas refer to the link provided below for some of the best colleges which offer courses in B.Arch in Hyderabad through distance mode of study. Almost all colleges offer part-time courses. You should be able to download their brochure to check if the institute offers distance education courses.
https://www.shiksha.com/architecture-planning/colleges/colleges-india?uaf[]=base_course&uaf[]=et_dm&ts=16911654&rf=filters&bc[]=5&ed[]=et_20