If I purchased a 5 gallon keg online could I carbonate the fermented beer by adding the required amount of priming sugar to the keg? Do I need a CO2 tank or will I be fine just carbonating it with sugar?
Beer can be carbonated in a keg but generally it is advised to use less sugar than one might use when bottling the beer. The problem being "gushing" or foaming beer being dispensed until the pressure drops. As a guide I use approx 140gr of sugar/glucose for bottling a 24L batch of beer, but I will use about 100gr of sugar to prime a 24L plastic keg. Of course if the keg become too carbonated then some pressure can be released via the keg cap. However towards the end of the beer in the keg, the pressure is usually greatly reduced and the cap must be loosened to be able to dispense the rather more flat beer.
Using a CO2 bottle to carbonate and pressurise the beer means it can be regulated more precisely and more gas can be added as beer is taken from the keg. That allows the beer to be fizzy until the last glass.
Beer in a keg is good for a while after the first beer is dispensed, for example it is a good solution to use during an evening party or afternoon BBQ. However if the beer is dispensed from a keg over a longer time (eg a week or more) then it can be useful to have a CO2 cylinder to repressurise the keg and to keep the beer fizzy and to prevent excess air entering the keg. If no gas is allowed to enter the keg then a partial vacuum will form and make dispensing the beer more difficult by reducing or stopping the flow after a time. Also any such partial vacuum will tend to de-gas the beer in the keg.
Of course kegs are perfect for dispensing beers with low carbonation like some British bitters and other ales but only for a short time. A few weeks is possible and in cold weather I have kept beer outside for a month in a keg while taking a pint every day.
I don't agree with some of the comments above. Keg conditioned beer has been made all over the world without CO2 gas for hundreds of years, and it lasted just fine in the cellars where it was made then! I have made keg conditioned beer and it lasted for a month from first tapping till I drank the last pint, and it was in a good condition for the whole stretch.
The keg must have a proper vent for this to work - if not you risk an explosion. Most brew kegs do have a valve and vent though - check!
Use half the priming sugar you would for the bottles. You then must leave the keg somewhere warm for three days at least. This will boot the yeast back into life and they will convert the priming sugar to alcohol + CO2. Then you must move the keg somewhere cool for 2 weeks at least to let it settle. Then you can tap it, and it should be ok. However I think that normally a month of ageing is better. Lager need much longer.
Priming with sugar works with kegs the same as with bottles, but it's better to use a CO2 cylinder for tapping. For priming, one should never use fixed amounts of sugar, but calculate the right amount (e.g. with this https://www.brewersfriend.com/beer-priming-calculator calculator). With the right amount of sugar, there should be now foaming or gushing (except when hop pieces are in the bottle or keg).
One can theoretically use a beer keg without a CO2 cylinder, but the oxygen will destroy and carbonation loss will make the beer undrinkable in one day after opening. For real tapping, one need a CO2 cylinder and a good tap (one with flow control or a normal one together with a spiral hose to reduce pressure). With the right pressure (if you are not sure, better use a higher pressure like 3 bar, but disconnect the CO2 directly after tapping to prevent over-carbonation), one can tap without foam problems and the beer in the keg will stay fresh even after disconnect from the CO2 cylinder and tap.
This largely depends on your keg type. If it is a cornelius keg, then priming with sugar is doable, but the first liter will also include most of your hibernating yeast. I run a small micro brewery, and have found my bottles require between 4-4,3 grams sugar per Liter (depending on style), but when I tap into Keykegs, 3,7 grams sugar per Liter is just Perfect for an IPA.
Keykegs are a nice solution that allows you to tap without CO2 available, as all beer is contained in a balloon inside the keg, and does not come into contact With whatever gas pressures the beer out (which is usually just air from a compressor). Keykeg demo