1 . Do all altcoins have an offline wallet generator ? For e.g does it exist for zencash, btcZ.. ?
what you call "offline wallet generator" doesn't have to be a complicated program designed to generate paper wallets for example. you can use literary any wallet that creates private keys and lets you export them to generate a cold storage.
for example in bitcoin you can download bitcoin core, go offline, generate as many new addresses as you want and export their private key to print, write down,... as your cold storage.
2 . Do all altcoins support signing transactions offline with the private keys, and then make them live using an online computer ?
it is impossible to answer this because altcoins are very different from each other an in order for a user to be able to do this, they have to add this option and make it easy to use. technically it should be possible for all the altcoins because basically you are splitting the steps needed to spend funds into 3 steps:
1. getting the UTXOs and making the raw transction to be signed online
2. signing the tx from step 1 with the keys offline
3. broadcasting the signed tx from step 2 online.
so the wallet program has to have the command (code) that does these 3 separately.
3 . With cold wallets, i would have to make a backup of the wallet each time i make an outgoing transaction ? or every 10 or
it depends!
some altcoins also follow the HD wallets thing that bitcoin uses so if you make a backup of your wallet or Seed or Master private key once you don't need to do it every time. but if they don't have HD capabilities then you will have to make a back up each time you
generate a new key pair not make a transaction.
About paper wallets > If you have a paper wallet and one day you need to use it, that day youll have to expose the private key online
when making a transaction ?
as i explained in answer to your second question it depends on the wallet. if it has the ability to sign offline (like most bitcoin wallets have) then you never expose your private keys online.