Say i put ubuntu on usb and boot from it and now generate 1 paper wallet using bitaddress.org gitup file locally and then instead of printing this i ssved it as pdf and then after booting back to windows i put this pdf in .rar file with secure password protection and save this file in mutliple places.Then even if i use the internet i won't be at risk right?
Why not encrypt it on your throw away USB stick OS? If you move the PDF unencrypted to a different machine it make no sense to set up the USB stick OS in the first place as it offers you no additional security.
is bitaddress.org paper wallet generation really random?
Yes, even on low entropy systems (e.g. new OS on SSD/USB stick). The mouse movements required at the start provide enough entropy to make the key generation random.
and last question if i have say 7 bitcoins on this digitally stored paper wallet and i want to spend 2 bitcoins from it and want to have 5 bitcoins in it.Can i do so?
Yes, if you are careful. More below.
because i have read somewhere that we need to sweep the paper wallet and why's that?Can't i just spend directly the amount i wish to spend?
P.S i don't want to print a paper wallet because i am too paranoid i may lose the paper or damage it
The "problem" with spending paper wallet funds are the software you use to do so. If you have 7 bitcoins received to a paperwallet, these 7 bitcoins are considered one or more inputs you can spend. Lets assume for simplicity you have only one input. You can think of it like a 7BTC bill or a lump of gold (I will go with the gold for this example). If you want to spend the 7 BTC lump you have to melt it down and create pieces of lesser value. Different wallets do this differently. Some would send the 5 BTC you want to keep (assuming no fee for simplicity) back to the address you previously had the 7 BTC on. Some would create an entirely new address for this. Its best that you prepare another paperwallet and manually send the lump you want to keep to it.
E.g. you have 7 BTC and want to send 2 BTC to Alice while keeping the remaining 5 BTC. You use the funds from your old paper wallet to create a TX that sends 2 BTC to 1ALICEvanity and 4.9998 BTC to 1myNEWpaperWALLET the remaining 0.0002 is used as fee.