If an alternator is labeled as 35 amps then theoretically it can output 35 amps into a battery
or other load. However depending on the alternator construction and how the maker rated it that does not necessarily mean that the alternator can do that continuously without burning out. That could be the max output at a low temperature. The safe output when it's hot and running continuously is likely much less.
14.4 V is certainly high enough to charge a lead acid battery. A fully charged FLA battery at rest (no load and time for voltage to settle after charging) will be about 12.6 V and less when discharged so plenty of differential for charging