Sure, but I'd make sure to use a regulated wart. Unregulated warts can run several volts above what is stated, especially with a low-amp load. I have a 12VDC 1A wart that puts out 23VDC with a 200 mA load. If you're concerned about run time with the AA batteries, you can also use a 3 D cell holder - same voltage (4.5) but way longer run time. Get one at Radio Shack for a couple bucks.
Yes and no. If it is a regulated power supply, then no problem as long as it can supply sufficient amps (overkill is fine). If it it not regulated then you need something designed for an amp range close to the draw of the device erring on the side of too much, not too little.
Generally, if it's being powered by 3AA's, it's not going to be pulling amps, but rather milliamps.
Anyhow, a DMM in-lilne with the positive wire on the battery holder will tell you what you want to know.
Also keep in mind, you can always get a supply that is larger than what you actually need. IE, if your device needs 150ma, you can use a wall wart that is 150ma or more. It could be 4.5vdc 10amp if you really wanted.