Hello and welcome to JustAnswer!
As long as there isn't a fluid leak then you don't need to check the fluid level. Checking fluid level requires a special dipstick, scan tool to read trans fluid temperature, and a chart to determine the exact fluid level for a given sump temperature.
Your noise could be a few things. It could be from abnormal tire wear or wheel bearings, neither of which are uncommon to make noise on these. When it's making the noise try swerving a little left and right and see if the noise changes. If it does change then you have a wheelbearing issue.
I've replaced a handful of transmissions on these for bearing noise also, but your description of a "low whining noise" makes me think it's more likely to be wheelbearing noise than transmission. The transmission bearing noise on these is generally a high pitched whining noise.
Is it related to vehicle speed? The faster you go the noise seems to get worse?
Does it make the noise only when you are moving? Or will it make the noise at idle or revving the engine up in park?
How old are the front tires, mileage wise? Was it making the noise before and after the tires were replaced?
The only time I hear it is when I am driving on the highway. The faster I drive the louder it gets. Only when the car is moving. Do not hear it when the car is in park.
Tires are no more than 5000 miles old. It did make the noise before the tires were replaced.
I first noticed the noise 2009 on vacation trip, but since I was told when I bought it that I didn't need to worry about the transmission and since there was nothing in the owner's manual, I wasn't too concerned. Until recently I had tranny problems in my other car and paid a sh!tload, I want to keep an eye on this one.
If you noticed the noise that long ago and hasn't progressed then there may be nothing to worry about. That would be dependent on how much you've driven it though, if it gets driven little then you may not have put enough miles on it in that time for it to get worse.
It sounds like tires shouldn't be the issue. I would still try swerving a little left and right and see if the noise changes. If not then a stethoscope or device called Chassis Ears can be used to verify where the noise is coming from and if it's actually coming from the trans. Assuming you don't have an all wheel drive model, a noise that happens when the car is moving is either coming from wheel bearings or the transmission.