Laptop questions...

[fee-is-me]

I have a laptop and i *think* i need a new battery for it AND i think there might be a problem with the fan inside.

I am a bit thick about techy stuff, hence these questions:

I think i need a new battery because when i unplug it, the battery only lasts for about 10 minutes without needing to be plugged in again and it used to last about an hour(?) - have i got this right, or am i doing something wrong and i don't in fact need a new battery?

The fan used to be quiet but several months ago it started making a strange noise when it 'stopped whirring' (a sort of grating noise) so i thought i should replace it. It has now stopped making that noise and seems to be 'quiet' again. I can hear it 'fanning' now but it won't make that noise. Is it cured or has it gone badly wrong and needs replacing asap?

I hope this makes sense to someone!