Electronic – Does using 220V-110V transformer matter

It's a little unclear what exactly you are trying to accomplish. If the point is just to experiment with full wave bridges and see all the signals, then do it at a low voltage like JonnyBoats said. You can probably find a old transformer somewhere that is rated in the range 6-12V AC at 1 Amp or so. That's a good size to put a full wave bridge after, and then you also get a useful DC voltage to do lots of other things with.

As Jonny mentioned, there are also wall wart type transformers that are rated for less power but you can do mostly the same things with. The advantage is that these things are cheap nowadays. You can probably find something in the 3-5 Watt range for $5. Jameco has a broad selection of such things. That's a good place to look around.

If you really want to experiment with a full wave bridge driven by a function generator, then you should power the function generator from a isolation transformer. These are 1:1 transformers meant to take line power in and put line power out, except that the output can float. These will cost a bit more since they are usually intended for 100 W or more. Sometimes they even come in a box with a line cord for the primary of the transformer and a regular output connected to the secondary. You simply plug the cord into a wall outlet, and the thing you want isolated into the outlet on the box.

One gotcha you have to be careful of with these things is that they may not come wired up fully isolated. I bunch of years ago I bought a 500 W "isolation transformer" that was just as I described above. I used it to float a device under test so that I could hook up a grounded scope to it at various places. The first time I touched the scope ground clip to part of the power supply there was nice spark and the fuse blew. It turns out there was actually a deliberate ground wire inside the isolation transformer box connecting the ground from the line cord to the grounds on the output sockets. That's not what I consider "isolation", but someone else apparently does. Once I disconnected the two sides of the transformer and carefully verified there was no conduction path, it worked as intended.

That won't hurt anything (until you put a load on there) but it also won't work so well. As you can see, the same current is going through both coils. The lower voltage on the primaries and secondaries means that the core is going to be less utilized, so they might be a bit more efficient, but basically you'll be stuck with roughly the same current rating and poorer regulation.

If (and this is a huge if) both transformers were identical you might be able to parallel the two secondaries and primaries (taking great care as to phase, or you'll release the magic smoke). The slightest difference between the two transformers (even a slight one or two turn error in manufacturing the primary or secondary) and a lot of current could flow between the secondaries (resulting, potentially, in a lot of heating).

It would be better if you could split up your load between the transformers, or just use a bigger transformer.