Short answer: do not play matchmaker with Li-ion batteries.
1) As explained in the comments, parallel batteries with different voltages and low resistances will probably catch fire and certainly destroy one another if connected for any length of time. Do not do this. You will cause a fire.
2) Batteries at the same voltage with different capacities will have to remain at the same voltage all the time because they are in parallel. In a perfect world, they would drain according to their capacity, remaining at equal voltages the entire time. This is not a perfect world. Because of things like internal resistance and general errors (both age and manufacturing defects can mess with the batteries specs), there is a high chance of overheating. I would strongly advise against trying this. If you were really desperate, I would use diodes on the terminals of each battery to make sure that the current is always flowing in the correct direction (away from the batteries). The voltage across the diodes will increase if the batteries voltages diverge, but the diode will (hopefully) be able to handle it. I would choose diodes rated to at least half the voltage of the largest battery just to be safe.
3) Batteries in series are, actually, largely fine. The voltages will add. In terms of which ones would drain first, it would be a bit complicated, but you should stop using them after the first battery in the chain is drained. That means that if you have a 100 ah and a 200 ah in series, you would only get 100 ah total. Once the first battery is drained, the internal resistance will rise and it will start heating up. This can result in cell breaches and the like. I would strongly advise against using them after this point.
If you have any problems with any of the batteries, dispose of them safely. They are very dangerous and not something to be toyed with lightly. For god's sake don't touch the terminals together either or you will wreck them permanently.