The fan can be removed, although ideally, you'll need 3-4 hands to do it
The cones should have a slot or 2, just off-centre, on 2-4 'sides'. Using strong tweezers or needle-nosed pliers, you'll need to squeeze the plastic between the slots and, at the same time, prise the fan up a little, so each hole clears the base of the cone, all while holding the heat-sink firmly.
Repeat for each corner of the fan. If/when you replace the fan, simply press firmly, so the fan-holes clip over the cones - and good luck
If you decide to stick with replacing the whole heatsink/fan unit, you'll need a thin plastic scraper and ease the blade between the CPU and heatsink - they're 'glued' together with the heatsink compound.
After removing the heatsink, you'll need to remove every trace of that compound from the top of the CPU. When fitting the new heatsink/fan unit, check the bottom of the heatsink as some have a 'compound pad' applied whereas others are just bare metal.
If your new one has a pad already fixed, then carefully read the instructions to fit. If it's just bare metal, check for any scratches or dents and remove them with fine-grit emery-paper, working down to a mirror-finish.
On 1 side of the CPU socket is a little lever, lift this up and it will 'open' the socket to drop the CPU into it - make sure the CPU is the right way round for the socket, otherwise everything will end in tears!!! When the CPU is in the socket, press the lever back down to lock the CPU into the socket.
Apply a tiny drip of 'Arctic Silver' thermal compound to the centre of the CPU. Press the heatsink to the CPU and twist the 2 together to spread the compound, then fix the clips to hold the heatsink down. Whatever you do, don't part the 2 units again.