There were many few seats available for technical education. There were few seats available for technical education.

Another version: "There weren't many seats available..."

There were manonly few seatvacancies available for technical education. There were only few vacancies available for technical education.

In simple terms I didgot a diploma rather than a higher secondary education. In simple terms I got a diploma rather than a higher secondary education.

In simple terms I did a diploma rather than pursue a higher secondary education. In simple terms I did a diploma rather than pursue a higher secondary education.

My Ddiploma. My diploma

I tookgot admission intted to a polytechnic institute. I got admitted to a polytechnic institute.

I took admissionenrolled in a polytechnic institute. I enrolled in a polytechnic institute.

When we finished thise course, our college gave us an equivalent certificate so that we may nowouldn't face any issues in undergrad admissions. When we finished the course, our college gave us an equivalent certificate so that we wouldn't face any issues in undergrad admissions.

"this" isn't quite right, since you didn't explicitly refer to the program as a "course" beforehand, so this is more or less a first-time reference to it in this way, hence "the" would be more appropriate. You can use "this" if you want to give emphasis to the fact that you're referring to it as a course, but since the main focal point of the sentence is the certificate, this isn't necessary.

When we finished this course, our college gave us a equivalent certificate so that we maywould not face any issues in undergrad admissions. When we finished this course, our college gave us a certificate so that we would not face any issues in undergrad admissions.

We can takeget admission directly into a 2nd year of undergrad if we had done 3 years of diploma. We can get admission directly to a 2nd year of undergrad if we had done 3 years of diploma.

We can take admission directly into the 2nd year of undergrad if we hadve done a 3 years of diploma. We can take admission directly into the 2nd year of undergrad if we have done a 3 year diploma.