Most case designs in the ATX standard will use a single 92mm-140mm at rear, 120mm-480mm at top or 120mm-480mm at front.
Yes, there are a few cases with multiple fan rear exhaust, but they are niche cases and very hard to find, definitely not a mainstream case.
Fans are fans. Has nothing to do with whether there is a radiator attached or not, so Yes definitely you can use the fans included with the AIO as intake fans or exhaust. I ran a 280mm AIO with its 2x 140mm fans as intake and 2x 140mm fans as top exhaust for years. You can mount the fans to push air through the rad into the case, or mount them inside on the back of the rad to pull air into the case, doesn't matter, as long as airflow is into the case if the rad is at the front.
Same as for the top. Doesn't matter push or pull as long as air goes out.
Push/pull is where you have fans on both sides of the radiator, so you can add fans if you wish, but it barely makes any difference. Push works better at high rpm, pull works better at low rpm, so push/pull covers the differences of both.