Can I apply for BE, B. teck after Diploma in distance learning?

Yes, you can apply for B.E. / B.Tech after Diploma but this is not accepted in all colleges. So, before applying for it, get clarity regarding it.

Yes, there is an option to opt for engineering after Diploma.

I didn't understand what are you saying about distance learning if you want to take admission to complete your B.Tech you have to do a Diploma or direct choose your colleges for B.Tech Good luck.