Cassettes single change

The MVP sums it up nicely- excellent reply.

Just to add that a Shimano 11-30 HG50 9 speed cassette is about a tenner on wiggle, and a 9 speed chain is 6 quid... have a go... not much outlay and you'll learn some essential bike maintenence skills.

Tip number 1- don't perform this operation on a newspaper on the dining room table if you want to keep your relationship as smooth as your gear changes!

You usually wouldn't add another cassette speed unless you also change your front shifter to accommodate the additional cog, otherwise you will have a ten speed rear set-up with a nine speed shifter. Mechanically you can do it but depending on which of your ten speed sprockets you decide to do without (11 or 30) you may not see the benefit of the additional gearing.

Normally you would change the entire cassette to gain the large toothed sprockets you are thinking of. In my experience in most "modern" cassettes the larger toothed sprockets, up to and around the sixth of seventh sprockets are fixed and it is normally the smaller toothed sprockets (12, 13, 14 tooth) that are not fixed and can be interchanged, if you have another compatible sprocket, with different tooth counts. For example I myself bought a 12-30 Shimano 10 speed cassette and changed the 12 tooth for an 11 tooth from a 10 speed 11-25 cassette I had lying around.

If you are thinking of a larger toothed sprocket (say a 30 or 32 tooth nine speed) then you will need to consider the length of your rear dérailleur cage and perhaps your chain.

Accommodating larger toothed sprockets (above 28 tooth) can be difficult with shorter cage dérailleurs, although sometimes not impossible, despite the manufacturers guidelines. A medium caged dérailleur can accommodate up to and (sometimes) past 32 tooth. I have managed to get a Sora medium caged dérailleur running a 34 rear and a compact 50/34 crankset up front on a CX style bike I use for messing around in the local woods. With a bit of fine tuning my gear changes are trouble free and to be honest I never run 50 Front and 34 Rear, there is just no need.

The new chain is an easy one to explain, as you are adding larger toothed sprockets in essence the chain route becomes longer to accommodate the additional teeth. It is usually good practice to change a chain with a new cassette anyway. If you don't change the chain, but manage to get it to fit the new set-up you can run the risk that in certain gear combinations the chain path is "stretched" beyond capacity and causes the whole drive train to lock-up.......can be nasty.

One last point on the chain, if you are going for the ten speed rear set-up, you will likely need a new chain anyway, the ten speed cassettes require a narrower chain than their nine speed counterparts.

Hope this helps.

As with the other replies it's the whole cassette, but also think about the basic mechanics of a bigger gear.

More teeth means you'll probably also have to change the chain at the same time, because of course it needs to reach a bit further. As well, you need to check the range of the rear derailleur. Normally on a road bike it will be a short cage, which is good to 28~ish. If you go beyond that, you need to swap the mech for a medium cage, or be very careful in how you change gears so that you're never on a big ring both front and back.

You probably wouldn't want 32, which is normally only used on a mountain bike, or on cyclocross in combination with a closer range on the front (36/46).

If you want more gears you need to change the shifter and the casette. You may get away with keeping the rear mech.

No.
If your cassette is 9 speed at the moment, you will have to stay at 9 speed unless you change most of the group set.
No....probably.
You may not be able to change the individual cogs in the cassette as they are often joined together (certainly for SRAM)
Also the gap between different ratios would be too large so it would not shift very well.
If you want to change the gear ratios you should buy a brand new cassette....you will need to find out if your rd is long cage or not, if it is you will be able to fit a 32t cassette.