The message probably means you don;t have enopugh space on iCloud to backup the Phone.
iCloud has a 5GB limit. If your backup is more than that then it won't be able to backup.
As far as backing up to your computer, just connect it to your computer, and assuming you have iTunes you can just click on the Backup button in the summary page for your Phone in iTunes.
You can follow the instructions posted by Ramzee.
As to why you can take less photos, probably because you've used more space up with different things. so there's only so much space left for your Photos.
You can look in Settings->General->Usage, to see how much space you have available as well as the App that's taking up the most space.
Also when connected to iTunes in your computer Check how large the "other" category is.
If its more that 1 to 1.2GB then you may have some corruption.
if you send a lot of MMS/SMS try deleting them.
to completely get rid of others you will need to restore your phone as new.
but take a look at the link.
Look at the link I posted above, It has many solutions for the "Other" problem. Including restoring the device.
To clean iCloud you can go to Settings->Usage->iCloud->Manage Storage.
You can see how much space your backups are taking up. And Delete them if necessarry.
Though the newer Backup should overwirte the older one when its performed.
If you have alot of stuff to backup it may simply not fit in iCloud, you can also select what you want to backup there so your backup file is smaller.