JEE Advanced

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.