1) What do these numbers mean?
- I assume it is the speed. But is there any way to use these numbers to approximate how many Bitcoins per day/week/month you would average. E.g. a 100MH/s would be 0.000001BTC or something?
You assume correctly. Those numbers represent how many times a second the device executes the hashing looking for a valid block solution. You can easily calculate the daily (or hourly, weekly, whatever timeframe) expected earnings for a device given its speed and the current network difficulty. The equation (simplified) is as follows:
25 / difficulty * 2^32 / hashrate / timeframe in seconds
So, if you wanted to know how much an Antminer S5 (1.155TH/s) would expect to make in a day if it were mining right now:
25 / 163491654908 * 2^32 / 1155000000000 / 86400 = 0.00355
2) If I got a USB stick ASIC device (I'm sorry, I don't know the proper term for these), does it run as long as the PC is powered? I.e. if the PC is in sleep mode, or running.
Those are the proper terms. A USB stick relies upon a host computer to execute the mining software and a powered USB port. Therefore if the computer providing the power to the port, or running the mining software is stopped, so too is your mining.
There are other miners out there (I mentioned the S5 above) that are self contained. You plug in a PSU and a network cable, then use a web browser to configure it. You can then turn off your computer.
3) What would be an estimated bandwidth usage for one of these? It's not an issue, but I would like to know whether upgrading to a slightly better internet package would be a smart move to account for more bandwidth usage.
Minimal bandwidth required. You're sending and receiving small bits of data from a mining pool. Unless you're running your own pool or a full bitcoin node whatever you have currently should be more than sufficient.
4) Do they need 24/7 internet access? I.e. if your internet drops for an hour, would it resume as normal, or would it need to be reconfigured/start from scratch losing an progress it had made.
If the mining software can't connect to the pool, then your mining hardware would be sitting idle. You don't need to reconfigure. One thing I want to point out here (and it's bold because it's important):
there is no such thing as progress. You aren't executing a progressive series of calculations the cumulative effect of which produce a block solution. A share either solves a block, or it does not.
5) If you were to recommend a cheap starting device, just to see how it works and if it is something that would work for me, what would you recommend? (Not really necessary, as hopefully the previous 4 questions should help me choose, but just in case there is a specific model which is better)
Well, what's your definition of cheap? $50? $500? $5000?
USB devices are exceedingly unlikely to ever turn a profit. If it's just a "for fun" thing, or perhaps a lottery ticket you point at a "solo pool" then have at it.
