You can measure voltage and frequency with either a good-quality multimeter (e.g. a second-hand Fluke 77 on eBay
or a plug-in "Kill-a-Watt" type of meter.
Cheap $5-$50 new no-name Chinese-made multimeters are usually not really safe for use on 230V
Personally, I doubt a 10% difference in voltage will be critical for any of those devices apart from the Japanese 100V items, that could overheat. n.b. EU supply = 230V+/-10% US supply=120V+/-5% so running a nominal 100V device at 126V might be cause for concern.
Japan has a mix of 50HZ and 60Hz supplies so I'd expect Japanese made 100V appliances to be happy with either.
Normally, you can never split a 40A supply to serve two loads rated for a 20A circuit. Except here.
This is an allowed exception for supplying oven/range loads. It's in NEC 220.55, referring to Table 220.55, Note 4:
The branch-circuit load for a counter-mounted cooking unit and not more than two wall-mounted ovens, all supplied from a single branch circuit and located in the same room, shall be calculated by adding the nameplate rating of the individual appliances and treating this total as equivalent to one range.
NEC 220.55 and Table 220.55 also includes some derating (or more accurately, permissive up-rating) that overrides the normal "125% for continuous" derate found in NEC 210.19(A)(1). It appears to be permissive. Speaking of 210.19, ThreePhaseEel points out
210.19(A)(3) Household Ranges and Cooking Appliances. Branch- circuit conductors supplying household ranges, wall-mounted ovens, counter-mounted cooking units, and other household cooking appliances shall have an ampacity not less than the rating of the branch circuit and not less than the maximum load to be served. For ranges of 8 3/4 kW or more rating, the minimum branch-circuit rating shall be 40 amperes.
Exception No. 1: Conductors tapped from a 50-ampere branch circuit
supplying electric ranges, wall-mounted electric ovens, and counter-mounted electric cooking units shall have an ampacity of not less than
20 amperes and shall be sufficient for the load to be served. These tap
conductors include any conductors that are a part of the leads supplied
with the appliance that are smaller than the branch-circuit conductors.
The taps shall not be longer than necessary for servicing the appliance.
Exception No. 2: The neutral conductor of a 3-wire branch circuit
supplying a household electric range, a wall-mounted oven, or a
counter-mounted cooking unit shall be permitted to be smaller than the
ungrounded conductors where the maximum demand of a range of
8¾-kW or more rating has been calculated according to Column C of
Table 220.55, but such conductor shall have an ampacity of not less
than 70 percent of the branch-circuit rating and shall not be smaller
than 10 AWG.
This also overrides the 125% rating by saying a 40A breaker can definitely supply two 20A ovens, and saying a 8.75KW-9.6KW oven is allowed on a 40A circuit.
Best Answer
It is in principle possible to run a 240V load off a 120V supply using a transformer.
However you must understand that transformers can trade off voltage for current but they can't magic power out of thin air. The feed supplying the transformer must cover both the power requirements of the load and the losses in the transformer. Power is proportional to voltage times current (if the power factor was 1 it would be equal to voltage times current).
In other words if a transformer is converting 120V to 240V then the input current will be more than double the output current.
The problem you will run into is if an air conditioner designed for the US market requires 240V then it probablly requires more power than can be supplied by a normal domestic socket.
https://www.frigidaire.com/Owner-Center/Product-Support--Manuals/?productCode=FFRH2522R2 claims that unit takes 11.3 amps, double that and add some overhead for the transformer and you would be looking at around 25 amps from your 120V supply. Regular domestic sockets in the USA are rated at at best 20A and more commonly 15A. Furthremore those are only intermittant ratings.
Sorry but you either need to find a smaller AC unit that will run off a normal doestic socket or you need to get an electrian in.