The AYCE package is for mobiles as opposed to dongles.
You can tether a mobile to a PC to use it like this, some mobiles even have apps which can turn the mobile into a Wi-Fi hotspot.
That's not really a replacement for "home broadband" though not least because the mobile won't give as strong a Wi-Fi signal as a proper router will and you need to position the modem carefully for best results e.g. near an upstairs window. So arguably you'd need a "spare mobile" for that which would always need to be charging. You can't really answer a call on it if you're hanging it out of the window to get a good signal.
The setup which works best is a dongle and a router. This then does replace "landline broadband" providing an "always on" connection piped around the house plus it also has ethernet ports etc. Or a combined box, but the only one on the market at the moment costs £249 (Huawei B593).
Three are only just rolling out 4G now. Their network is actually what they call 3.9G "ultrafast" which is AKA "dual channel HSPA" or "DCHSPA". It's not the same thing. It's more like "fast 3G".
To answer your questions:
1. For DC-HSPA: between 15Meg and 25Meg downstream and 3Meg and 4Meg upstream. For 4G, I'd suggest upwards of 30Mbps downstream.
2. There is no "lowest speed" as such - all depends on how many use it. Three 3G DCHSPA here manages between 12Meg and 21Meg down and 3Meg to 4Meg up just about all the time (E3256 DC-HSPA dongle). That's because it's a rural area and not many use it (clearly, for it to attain those speeds, the maximum is 42Mbps down 5.7Mbps up). The same equipment in an urban area even right next to the mobile tower might struggle to attain more than 2Mbps downstream. It also tends to slow down a bit when the kids are off school. Finally, AFAIK, Three throttle certain types of traffic such as P2P down to levels at which it is almost useless. On the other hand, we can use it to stream HD TV here.
3. Latency on a good DCHSPA connection will be somewhere between 30ms and 45ms - by that I mean strong signal and little contention. It does however have a fair amount of "jitter" and can spike e.g. a ping bbc.co.uk -t will return 30 to 40ms most of the time with occasional upward spikes. An antenna helps with signal and with latency as does being near to the cell. You can find your local one at
http://sitefinder.ofcom.org.uk. Personally I'd have thought it would frustrate gamers. 4G is better, but this is only at the rollout stages. We have EE 4G and even with a moderate signal latency is more in the realms of 20 to 35ms.
4. With a dongle, whatever the package limit is e.g. 10GB/mo. With a mobile tethered to the network AFAIK it is unlimited, but it is unlikely to attain the same top speeds as a dongle/router combination and may have slightly different throttling because it is not designed for use as a "home broadband" connection. In case you wondered, no, you can't put an AYCE SIM card into a dongle, Three actively detect this and block the SIM.
At best, 3G is more than capable of walking all over ADSL for speed in both directions unless you live right next to the exchange.
Also at best, 4G is comparable with VDSL "Fibre to the Cabinet" and more capable upstream (see speed test just below, that's with only a 2 or 3 bar signal).
Most especially so in a lightly populated area with few using it. In a built up area with hundreds of phones connected to either, getting those sorts of speeds on a regular basis might be a pipe dream. And unlike a good FTTC connection with a good ISP where you might expect the same sorts of speeds all the time, both 3G and 4G are very variable and unpredictable.
However if you want to use a lot of data and have quick speeds, 3G and 4G are probably not best advised.
Would always suggest trying on PAYG first before committing because the overall summary is that you can't know until you try it.