"To go along with this question, what is considered the max amperage you can pull from a battery? My thinking is that you'd have to have enough batteries in parallel if you wanted to run something that pulls a lot of power, even if it is only for a short time. Also, what is generally considered the max charging amps? I'm thinking lead acid here, nothing fancy."
Most full size batteries (like those in a full size car or pickup) can put out a great deal of amperage, even beyond their rating, the main issue is you loose a LOT of potential Ahrs when you draw current faster. Most branded batteries will state their cranking amps or their Amp Hours (deep cycle) Generally each full sized battery at a minimum will be able to safely put out 200amps, most are capable of 500 or even 1000amps. Again you loose a great deal of capacity when drawing at these rates.
As for charge rates you can charge at almost any rate but again there is a great deal of losses and much more wear on your battery when you do this. Generally if you have a battery of say 200 amp hours you could charge up to a rate of 20 amps without excessive wear or losses, most however stick to C/20 or about 10 amps for a 200ahr battery. Higher than that and you loose much more energy to heat and wear the battery faster. It is also much more difficult to determine state of charge when charging very rapidly and the likely hood of overcharging is very real.
An important note...
There are methods of equalizing or restoring battery capacity, I would recommend this before just using batteries in poor condition.
One method is to use a battery discharger (usually a 500amp is good) and recharge rapidly several times.
Another method is to drain some electrolite and add dissolved Epsom Salts (method can be found on the citicar yahoo group files area) This will dissolve the sulphation and increase the batteries ability to charge / discharge but also increases the internal self discharge rate.
Another method is to discharge the battery and use a pulse charger to recharge the battery several times. You can build a bedini battery charger to pulse (slow but easy) or you can build a faster 555 like they had in home power.
Lead Acid Battery Desulfator
To revive your weak but functional batteries, there is also a paper floating around on battery building and repair (aka dissassembling and repairing lead acid batteries)
Good Luck