Great!
Yes I do have the manual.
Hi Tony.
Great that you have the owners manual as that will list the recommended intervals for various preventative maintenance services, like the ones you listed.
My online product application guide lists two available engines for your 2010 Corolla; a 1.8 and 2.4 liter 4 cylinder engine. For either engine the Toyota recommended and preferred oil viscosity is 0W-20. This viscosity is a synthetic oil that Toyota is recommending to be used in these engines. Is your Corolla equipped with the 1.8 or 2.4 liter engine?
Below is the link you can use for my online product application guide that lists the recommended oil viscosity, filter part numbers, spark plugs, component fluid capacities, etc. It's free and can be used for any vehicle -
http://www.amsoil.com/mygarage/vehiclelookup.aspx?i=1&zo=349698
You can use any oil or filter brands you wish, but be advised as with anything there can be significant differences in the quality and performance of these products from brand to brand. AMSOIL synthetic motor oils pioneered the synthetic lubricants industry for cars and trucks way back in 1972 with the worlds first 100% synthetic API qualified motor oil and is known as, "The First in Synthetics", (TM). AMSOIL, (pronounced AMZ-OIL), has over a 40 year history of manufacturing the highest quality products of their kind in the world and is the worlds largest pure synthetic oil company. I've been an AMSOIL Dealer for close to 30 years and it will be my pleasure to help you out with anything you need. Send me a private message and I can get you the lowest prices possible for AMSOIL that are much less than competing products. For anyone else that is interested, feel free to private message me as well.
As for changing oil and oil filters, yes I strongly recommend the oil filter be changed every time an oil change is completed as that oil filter holds some old oil in it, so adding new oil to old oil, well not so good. It would be tantamount to taking a shower with your socks on. :no:
Below is a link to my Performance Tests page and you want to click on the first test result listed - - "A Study of SAE 5W-30 Synthetic Motor Oils". This will give you an idea of how many popular brands of motor oil compare to AMSOIL in a battery of standard oil industry tests.
http://www.amsoil.com/performancetests.aspx?zo=349698
Below the first test listed are many other test results including field test results and they are very eye opening as to the substantial differences and results that can be had with differing brands of motor oils.
As to oil filters, below are the results of a standard industry oil filter efficiency test comparing the AMSOIL Ea Absolute Efficiency oil filter with several other brands, including the Toyota oil filter -
Here is a picture showing the high quality construction of the AMSOIL Ea oil filter -
Here is a 5 minute video from my HiTechOil YouTube channel that will tell you a lot about molor oils and what exactly synthetic oils are. There are many other related video's on my YouTube channel, so feel free to browse and learn -
I take it you are the original owner of this Corolla and are familiar with its maintenance history?