Impact Wrench

Go to the manufacturer's website for their recommendation on tire rotation.

As for taking the tires off - impact wrench works great. Just have to make sure the electric impact wrench has enough torque on it, as the starting torque to break them free can be pretty high.

If you don't have one - 4-way tire wrench, tire iron, breaker bar, etc. will also work well - anything that can give you a little extra leverage to help break those lugs free. Regardless of how you take them off, if a lug seems "stuck", hit it with some penetrating lube first to help loosen it. Otherwise you could risk snapping the lug off/breaking the wheel stud. Happens to all of us at some point.

When it comes to put the wheels back on, use a wrench (tire iron, 4-way wrench, etc.) to tighten them, then use a torque wrench to finish the tightening sequence. 76ft.lbs. is what is called for in the manual.

Never use a torque wrench to loosen nuts, only to tighten them.

I wouldn't - most don't have a good way to limit the torque they put on the lugs. You should always hand start the lugs to prevent cross-threading anyways. From that point - pretty easy to hand tighten them.

You can hand tighten them pretty far, probably depends more on your finger strength. I start out the lugs by hand, get them all snugged up, then I wiggle the wheel a bit, tightening them a bit more. At this point, the wheel will have very little movement to it. If you use the torque wrench at this point - might be less than a full rotation to get them properly torque.

No issue using the torque wrench to tighten them - usually that long lever arm of the torque wrench will be annoying and you can use a 4-way wrench or regular ratchet to get it make good contact with the hub and then finish it of with the torque wrench.

Jack stands - pretty much any of them will work for the Corolla. Even the least expensive jack stands are rated for 2 tons+. Most get them bundled with a trolley jack or floor jack. The better jacks usually have a much wider base and are inherently more stable, but you also have to account for the reduced amount of room to work with, once it is on the jack stands. How level the garage floor is, what material it is made of, how often you'll be using the jack stands, etc. will all factor into this. For some DIYers - $20 set of Pro-lifts will be perfectly fine, others will need to use some US-jack or HF or OTC branded ones - looking at $200 each or more. I've only used jack stands to help take some load off the hydraulic jacks, never to full support the weight of the car - so as a secondary safety measure, these cheap-jacks are find for my home use. At the shop - we use OTC, as we are under the car a lot - can't really put a price on safety in this particular case, as many times the jack stands there are the sole device to lift up and hold the car.

OTC equipment in general is pretty expensive - they are the professional grade tools. I just mentioned their name for comparison sake - not to imply that this is what a weekend warrior should by to work on their car. For a shop - that is a completely different story. Now you have to make sure tools can stand up to the rigors of constant use as well as provide ample protection to the employees, from the liability standpoint.

As for other reasonably priced jack stands - some have mentioned Sear's has some decent 4 corner jacks.

Lots of ways to rotate tires - depends on what equipment you have and how much time you want to spend on it. You don't have to buy any equipment at all, if you want to use what you already have. Without jack stands or floor jack, you can rotate your tires using the factory scissor jack and the compact spare tire. Lift up one corner of the car, remove wheel, replace with compact spare, lower that corner - go to the corner you want to swap the tire with, jack it up - swap wheels, lower corner. Go back to the corner with the compact spare - swap it with the wheel. Repeat for the other corners.

Of course, that method will take a lot of time - for impatient people like me - I'll use the floor jack and lift up one side of the car, swap that side, drop the car - repeat on the other side. Need a fairly beefy floor jack to do this and some experience. Need to find the balance point on the car, otherwise you will not be able to lift up the car smoothly, likelihood that something bad will happen.

I don't know of many people that try and lift the entire car off the ground to rotate the tires - I wouldn't recommend that unless you got some seriously strong jack stands. The biggest issue is lifting the car onto the jack stands. Ideally, you want to do it all at one shot, think garage lift - but at that point, why bother with the jack stands. Picking it up at each corner or as an axle pair can cause excessive side loading which can collapse or topple a floor jack. That's there is a big warning label on them to only be used in matching pairs, never to support both ends of the vehicle simultaneously.

I personally never fully rest the weight of the car on the jack stands, as I use them exclusively as a backup to my floor jack. I trust the hydraulics on my floor-jack more than I trust my cheap jack stands - this being that I know what the floor jack can do, don't have any idea how much side loading my jack stands can tolerate. I know this is counter to the prevailing attitude with most mechanics - most trust the jack stands, not the floor jack. I totally agree with this - but if you saw my floor jack, you'd understand.

If it was the other way around - like if I used a cheap trolley jack - then yes, I'd invest in some heavier duty jack stands and use them to take the full weight of the car, use the hydraulic as a secondary. At the shop, everything has to be mechanically locked for safely - can't rely on any hydraulics, everything is backed by some sort of mechanical bridge or jack stand.