JEE Advanced

First of all, you cannot appear for JEE Advanced without clearing JEE Mains. For clearing JEE Advanced you need to clear the JEE Main exam and secure a rank among the first 2,50,000 as per the merit list. Once you clear JEE Main exam you are eligible to appear for JEE Advanced. JEE Main is conducted for providing admission to the National Institute of Technology, Indian Institutes of Information Technology, and central or other government Institutions all over the country. JEE Advanced is conducted for providing admission to all Indian Institutes of Technology (IITs). JEE Main and JEE Advanced are both exams are conducted at the national level. If we compare both exams, JEE Advanced is a little tougher than JEE Main exam. I hope this will help you.

There is a list of colleges where you can get admission through the TS EAMCET scorecard.
1- VNR Vignana Jyothi Institute of Engineering and Technology for computer Science and engineering branch.
2- Siddhartha Institute of Engineering and Technology, Hyderabad for electrical and electronics engineering.
3- University College of Engineering, Osmania University for electrical engineering and mechanical engineering.
4- JNTUH College of Engineering, Hyderabad for Civil engineering and mechanical engineering. For more details, you may visit the Shiksha college predictor link (https://www.shiksha.com/engineering/ts-eamcet-college-predictor). There is a list of colleges where you can get admission through JEE Mains scorecard.
1- National Institute of Technology, Raipur for mechanical engineering.
2- Moulana Azad National Institute of Technology for mechanical engineering.
3- Malaviya National Institute of Technology, Jaipur for civil engineering.
4- National Institute of Technology Calicut for chemical engineering. For more details, you may visit the Shiksha college predictor 2022 link (https://www.shiksha.com/engineering/jee-main-college-predictor). In engineering college, Branches totally depend on your interest because all branches are good in their own way.

The answer vary as the definition of good college depends on you, I know some who are repeating even after getting 4k rank in JEE Advanced. Let's make a list of good options ( in my opinion)
Creamy layer (CSE, ECE, electrical, mechanical)
NIT Trichy
NIT Warangal
NIT Surathkal
Better NITs ( CSE, ECE, electrical)
NIT Allahabad ( chemical is also famous branch of Allahabad because of its location near chemical industries of Uttar Pradesh)
NIT Rourkela
NIT Jaipur
NIT Calicut
NIT Nagpur
Other good NITs ( only CSE and ECE)
NIT Bhopal
NIT Surat
NIT Jamshedpur ( mechanical is a good option because of location)
NIT kurukshetra, Jalandhar, durgapur, Hamirpur, Delhi
NIT Patna
Other NITs
Okay, now let's discuss the cutoff :- ( all cut-offs are for other state)
Creamy layer (upto mechanical)
General = 9900 Marks= 175
OBC NCL =3300 Marks= 154
Better NITs ( upto electrical)
General= 12500 Marks=155+
OBC NCL= 3900 Marks 142
Other good NITs ( upto ECE)
General=20000 Marks= 141
OBC NCL=6000 Marks=134+
Here the marks mentioned are approximated using the last two JEE Main sessions ( Jan and September 2020). The marks required for EWS and OBC candidates are almost parallel for all india quota so one can get the idea for EWS.

Yes you can give the JEE Advanced 2023 after qualifying the JEE Main 2023. The eligibility criteria is given below.
1. Age : The candidates should have been born on or after October 1, 1998. SC, ST, and PwD candidates are given five years age relaxation.
2. Number of attempts : A candidate can attempt JEE Advanced maximum of two times in two consecutive years.
3. Appearance in Class XII (or equivalent) examination : A candidate should have appeared for the Class XII (or equivalent) examination for the first time in either 2022 or 2023 with the subjects Physics Chemistry and Mathematics. Candidates who have appeared in the Class 12 examination for the first time in 2021 or earlier can also apply for JEE Advanced based on the special relaxation criteria.