Should I get a purifier designed for a room larger than the room it will be used in?
Ultimately that is up to you, but there will be no drawbacks in the functionality of the unit. In fact, a larger unit will potentially cycle the air in the smaller room more times each hour, meaning your air will get cleaner faster. Just make sure the room you have is not larger than the purifier's designated room size or it will not properly circulate all the air in the room. Keep in mind though, that larger units often have a higher price point than smaller units.
If I get a larger purifier, will it work in multiple rooms?
A purifier will only ever work in the room it is in. It will work in completely open space, like a studio apartment or when two rooms open completely into another, such as a living room and dining room, but it will not clean the air of two separate rooms if those rooms are separated by walls or door ways, even if the doors are kept open. You can move a unit from room to room as necessary to clean different areas, but make sure that you leave it in any one room for at least a few hours for it to have a noticeable effect. And be aware that contaminants may start to accumulate in a room again after the purifier is turned off or removed.
What's the difference between True HEPA and HEPA-like filters?
Most purifiers use particle filters but "HEPA" is a specific designation giving to certain types of particle filters. To qualify as HEPA, as designated by the US government standards, a filter must remove 99.7% of all particles 0.3 microns or greater from the air that passes through it. HEPA is considered the industry standard for particle filters and will do the best job of filtering particles. Within the HEPA classification, some filters may actually offer higher levels of efficiency, but to qualify as HEPA (sometimes referred to as True HEPA) they must meet this standard. HEPA-like filters are particle filters that have a similar design but do not meet HEPA standards. Some HEPA-like filters can be very close to True HEPA standards, while others are very far removed. Many purifiers will use HEPA-like filters but still claim a 99.7% efficiency due to other features of the machine improving overall particle capture. For example, a machine may use a HEPA-like filter and an ionizer, or an electrostatic HEPA-like filter to get comparable results. A true HEPA will achieve these standards on its own, without additional devices.