Colleges in Tirupati

According to AP EAMCET 2022 cut off ranks for Veterinary seats for SC(women) students are as follows
1. AU Region-
a. for non-farmer category: women-3200-3300
b. for farmer category: women- 4300-4400
2. SVU Region-
a. for non-farmer category: women-3000-3100
b. for farmer category: women- 4200-4300
3. Un-reserved region
a. for non-farmer category: women-3100-3200
So according to this cut offs I don't think you can get free veterinary seat by the mentioned rank through AP EAMCET

You can consider following:
Rank 1 - Sri Venkateswara University College of Engineering, Tirupati
Rank 2 - Sree Vidyanikethan Engineering College - [SVEC], Tirupati
Rank 3 - IIT Tirupati - Indian Institute of Technology - [IITTP], Tirupati
Rank 4 - Sri Venkateswara College of Engineering - [SVCE], Tirupati.

APLAWCET cutt off for SPMVV is around 675 ( open category). So you have fair chances to get SPMVV.

EAMCET is an entrance exam conducted to get admissions in engineering colleges and medical colleges.
The cutoff rank for BC b category in Sri Vidyaniketan Engineering college are
CSE : 17000
INF : 67000
As your rank is 30000 you are eligible for Information technology branch in Sri Vidyaniketan Engineering college, Tirupati.
Hope this will help you. Good Luck

APICET (Andhra Pradesh Integrated Common Entrance Test) is conducted for admission into MBA and MCA courses in colleges of Andhra Pradesh. The last rank for free admission through APICET varies from year to year, depending on various factors such as the number of seats available, the difficulty level of the exam, and the number of candidates who appeared for the exam. So it's difficult to say last rank.

Yes, You can take admission for B.Sc Psychology in SV University. They offer for B.Sc Psychology course.

Sorry to say that you cannot get seat in Sri Venkateswara University Tirupati
As the cutoffs are very high for CSE branch
The closing rank are 1600 approximately for CSE in SVU
Based on previous year statistics
Anyway
You can get many other colleges so do not worry
Vidya Niketan college of engineering is good.