Can you explain SDHC memory cards to me?

There’s class 1, Class 2, and Class 6 that I’ve seen on one search. What is the difference between all these classes? Are there classes 3 through 5? Why are the earlier classes still sold?

What about microSDHC cards? Are they usable in cameras if you have the larger sleeve to put them in? Or are they only for slots that take that size card, like in cell phones?

If you get a larger microSDHC for your phone so it can have more memory, is there anything essential on the old chip that must be copied over, or do the chips only contain content?