Having bought the car just two months back with 99965 miles on it I took it for a spin on the weekend travelling from Houston to Austin and back.
I filled the tank before leaving and was back next day having clocked 413 miles. Went to the gas station and filled up - 11.59 gallons before pump shut down . The average was 35.63. Within Austin I drove about 50 miles which surely cannot be compared to the highway driving where I was doing between 65 and 70 mph almost all the way to Austin and back the next day with cruise control engaged. I have been getting 30 mpg in the Houston city driving. So if I take that into consideration my highway average should actually be around 37-38 mpg. Not bad in many way’s but there may be room for improvement. I had the air filter replaced last week and maintaining cold tire pressure of 30 psi. I did not use the A/C either way since the temperature was in the vicinity of 50 - 55 F.
Someone suggested to me that I should replace the pcv getting it from a dealer and not from autozone. Wonder why it was so suggested. Is it a DIY operation? How much does it cost?
On cold mornings (40 F) when I start the engine it idles at around 2000 rpm and once I drive away and engine warms up it idles at around 500. I feel that my engine is slightly retarded but not sure. I changed the oil/filter after doing 3750 miles.
Since I bought it I have done about 5000 miles and and except for a bad battery which I changed yesterday to Duralast Gold, it is running OK.
What else is there for me to check to ensure trouble free performance.
Check The Owner’s Manual For Some Ideas.
If you don’t have the manual, get one.
Some fluids should probably be drained and filled.
I guess your car has a timing chain instead of a belt, so replacing the timing belt is not an issue. Replace the serpentine belt if you can’t determine if or when it was last done.
You are getting 30-35 MPG, that’s about what to expect in real world driving. According to the EPA you should be getting 25-36 MPG depending on transmission and type of drving. The mileage you are getting falls within the estimates. There is probably nothing wrong with your car.
Corollas are on a 30/60/90/120K service schedule, so you need to determine what service, if any, was performed around 90K. If not, plugs, coolant change, ATF fluid exchange (if AT), PCV, brake fluid flush are all indicated. I have found that changing air filters every 20K is better than waiting the full 30K.
Our Corollas seldom got better than 37 mpg on the highway, so you are well within a normal gas mileage range. They are extremely reliable cars if kept up to the owner’s manual standard.
OEM plugs are good for 120k miles. Even though the transmission fluid is supposed to be good for life, it isn’t so I would get it changed now and every 30k from now on.
As far as your mileage, its about as good as it get with this model.
Elaborate please on “I feel my engine is slightly retarded”
This data would indicate that your engine is running beautifully, especially for one pushing 100,000 miles. With respect, you’re obsessing.
Get all the scheduled maintenance performed, monitor your fluid levels (with a 5 year old car of unknown history replacing the oil and coolant would be prudent), and treat the car well and you should have many trouble free miles out of it.
Relax and enjoy the ride. Stop obsessing.
I had forgotten about extended plug change intervals on the newer Corollas.
From my personal experience on my Mazda MPV, lifetime ATF is a no-go. My fluid needed changing well before the 65K miles, when I realized I had not changed it yet. This is one manufacturer’s standard that I think they need to do more real, on the ground research on.
Thanks for heads up on the manual, I have that on top of my list. How about those service manual’s available at Autozones - Haynes. Is that better than the original manual?
As for the sepentine belt I will keep that in mind
Thanks
By retarded I mean the car stalls at traffic light sometimes unless I rev up and take off.
I appreciate your comment and the fact that I may be a hypochondriac. Nevertheless, I did mention that I had changed the oil but yes the coolant is next one to change. Next weekend I may get it done. I plan to do it myself to save a few pennies 
Is that something which many do?
The Service Manual Is A Good Idea. Additionally, I would Keep A Genuine Owner’s Manual In The Glove Compartment. It Should Have Never Been Removed.