UPCAT

I have no idea about paid seat but yeah their are some seat reserved for reserved categories candidates for more details please visit UPTU official website and download pdf format of reservation broshchere.

Yes, there are:
1. Inmantec Institutions
NH 24, Near Dasna Crossing, Adhyatmik Nagar, Udyog Kunj, Ghaziabad, Uttar Pradesh 201009
2. I.T.S College Ghaziabad
Grand Trunk Rd, Mohan Nagar, Ghaziabad, Uttar Pradesh 201007
3. IMS Noida
A-8 B IMS Campus Sector-62, Noida, Uttar Pradesh 201303
4. Galgotias College of Engineering and Technology
1, Knowledge Park, Phase II, Greater Noida, Uttar Pradesh 201306
5. IMS Ghaziabad (University Courses Campus)
IMS GHAZIABAD (UC CAMPUS), NH 24, Adhyatmik Nagar, Ghaziabad, Uttar Pradesh 201015

Yes, you can get admission in the second shift.

Direct admission is not appreciated.
You should choose SRMCEM in the counselling procedure for AKTU and you will be allotted college if you are eligible.
The study atmosphere in this college is very pleasant and faculties are well experienced.
Placements are good as well.

No, the result of UPSEE/UPTU will be declared in the last week of May.

Hello Ayush,
You have to score more than 300 marks to get average rank in range of 15k to get college in UPSEE.
You can check college details by this link:
https://www.shiksha.com/b-tech/resources/upsee-college-predictor

There is no relaxation in marks for girls. If you want a good college, you need to get a rank in top 5000 but at 220 marks, there are fair chances of ABES and AK Garg College. They are good private institutes.
Best of luck.