Using my 110-120v American appliance in 127v Rio

Check the label/plate on the unit. It will tell you how restricted you are. If you buy equipment in most of the world it will take 110 to 240 volts without issue but the US was way behind the last time I looked. However, they may have managed to catch up over the last few years.
The frequency is 60 Hz in both countries but the plug type is different.

I have many 110 v plugged into the 127v with no issues. You do have to get an adapter for a 3 prong cord or some stores have outlets you can change to.
I found her not many old outlets were grounded, but they work.

No earth is only a fatal issue if something goes wrong.
That happened to a bloke I knew (note the past tense).

No earth - fix the socket or rewire the house.

This only matters is the item should be earthed.

Most likely no.  I've done before.  Short term, no need.  Long term usage, maybe.

It's not the voltage.  It's the frequency that matters. 

If they specs here are 60Hz, and your stuff works on 60 Hz, then it won't fry.

Most UL  rated and certified power tools, appliance, consume electronics are devised to some range latitude in voltage.

Off course, if you plug a 110 V ( Single Phase ) in a 220 V ( tri phase ) outlet, then you are asking for trouble.

The only real problem you will deal is outlet matching your power chord prongs.  Which you can work around by buying an adapter at a retail store.