You mum has good reason to worry about second hand tanks leaking. Some do and some don't.
You can buy a second hand tank but try to get one that is set up and has water in it so you can see if it's leaking. Quite often you can buy a complete aquarium with filter, fish, plants, ornaments, etc, and they are the ones to look at. Or if you are checking out empty second hand tanks, ask the seller to fill the tank with water before you get there so you can check it for leaks.
Check the stand too. Chipboard/ particle board cabinets are crap after a few years and once they get moisture on them they start to fall apart. Look for bits of particle board bubbling or lifting or any swollen areas where the wood is slightly thicker than normal. These areas are water damaged and the stand will need repairing or replacing.
The stand should be solid enough and not move if you climb on it. A 4 foot aquarium with water will weigh over 150kg, the average human weighs around 70kg, so the fish tank with water will weigh a lot more than a human. If you can't climb on the stand or sit on the stand without it wobbling, then the stand is stuffed.
Check the joints on wooden stands and make sure there are no gaps between the wood. Sometimes the screws/ bolts loosen up a bit and the stand can be repaired simply by tightening things up and adding a few cross members and some more screws.
If you get a metal stand, check it for rust. Some people paint over the rust and sometimes the rust hasn't come thru yet. In which case you will often see blisters/ small bumps under the paint, or the paint might be flaking off. The rust is most common on the bottom by the feet, and in the corners or anywhere there are joins.
Don't confuse the welds on metal stands for rust. The welds are in the corners of the joints and should be a little bumping but they only run along the join. Rust can be anywhere.
Ideally you want to see the tank full of water while it is on the stand. Then you can check the silicon and give the tank and stand a gentle push to see if the stand moves. Be very careful doing this because if the stand is wobbly the entire thing could collapse.
If you buy a tank with fish and plants you can sell/ trade the fish to a petshop for store credit and use the credit to buy something else.
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When you look at second hand tanks, check the silicon (the glue that holds the glass together). Good silicon should be reasonably clear and firm but squishy when you touch it. If the silicon is white or has air bubbles in it, or the silicon is hard and brittle, then it is stuffed. You can usually see the bubbles between the sheets of glass where the silicon goes white because it is coming away from the glass. You can try grabbing the silicon with your finger and you should not be able to. If you can pull the silicon away from the glass it is stuffed.
If the silicon is blue it simply means it has been stained with a medication (usually Methylene Blue). Stained silicon is fine as long as it doesn't have bubbles in and meets the requirements mentioned above.
Some aquariums have black silicon and this has the same issues as above.
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If the silicon is stuffed you can remove the panel and glue it back on. Little tanks are easier to do than bigger tanks and you might be better off finding a pet shop that builds or repairs tanks and they can cut the side off and glue it back on. If the silicon is damaged on all sides and corners it will probably be cheaper to get a new tank compared to having someone else rebuild it. However, if you are reasonably handy, you could try regluing the tank. You remove one side with a single sided razorblade, they have a smooth side for holding and a sharp edge for cutting. You remove all the silicon from the glass and wash and dry the glass. Then apply some "Glass Silicon" so it covers the edges and put the sheet of glass back on. Use some tape to hold the glass in place. Make sure the edges line up. After 24 hours you can remove the tape. Wait a week for the silicon to fully cure before filling the tank up outside and checking it for leaks.
The hardest parts to do are the top cross members and these can be difficult to remove.
If you have to reglue several or all the sides, cut two sides out and do them at the same time. Don't put a full bead of glue on the ends where the 2 side pieces join the rest of the tank. Just put a couple of dots of silicon so you can cut it off when you do the other 2 sides.
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If a tank leaks, it does not necessarily mean the entire side will come away. And sometimes you can have tanks that don't leak and the entire side does come away. This happened at the local petshop last year when the front panel of glass came away from their discus tank. The tank as only a couple of years old and the silicon used turned out to be a bad batch. Subsequently 400litres of water, gravel and thousands of dollars worth of fish ended up on the floor. Surprisingly all the fish survived.
Personally I have never seen nor had a pane of glass come away from any of my aquariums, but I have heard of it happen to a few people. I have had tanks drip/ leak and I patched them with glass silicon and they were fine.
If you check the silicon for cream/ white or opaque discolouration, this should not happen. And look for air bubbles where the silicon meets the glass.
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If you check out the new tanks & stands, and the actual fish tanks with fish in at the local pet shop, you will be able to see what the silicon on new tanks looks like. You will also be able to check stands/ cabinets and see how smooth and flat everything is. You can then use that information as a guide to looking at second hand tanks and stands. If the second hand items do not look similar to the new stuff (around the joins, etc) then there could be issues.
Be careful buying any tank with curved glass. If the glass cracks it can be very difficult to replace and you usually get a new tank.
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If you buy a second hand tank, make sure it is completely empty before moving it. Do not have anything in it. Put the tank on a couple of thick blankets or a foam mattress in the back of the car, or across the back seat if there is room. Put the other items in a bucket or box and put them in the car but not in the tank.
If you get fish, plants, etc, with the tank, take several large buckets or plastic rubbish bins and put the fish in one, plants in another and gravel in several others. If the tank has a power filter try to keep that wet. Most external canister filters have taps that you can turn on and off. You can turn them off and it should keep the water in the filter and that should help keep the bacteria alive as long as you keep it out of the sun and don't leave it off for more than an hour or two.
I usually half fill a plastic rubbish bin with tank water, add fish and put the filter on that bucket. Then gravel clean and empty the tank and load it into the vehicle. Once everything is packed and money has changed hands, turn the filter off and put the fish and filter in the car. Then head home. When you get home take the fish and filter inside the house and turn the filter on. Top up the bucket with some dechlorinated water and then start getting everything out of the car.
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African Rift Lake cichlids come from hard alkaline water. Central & South American cichlids generally come from soft neutral to acid water.
You can keep some fish with cichlids but it depends on what cichlids you keep and how big they are. All cichlids are territorial to some degree and some grow big, over 12 inches. If you keep small African Rift Lake cichlids you could have rainbowfish in with them but not much else.
Generally in hard alkaline water it is Rift Lake cichlids, rainbowfish or livebearers.