@garbus
The complete answer to this would require a lot of text. You would probably do well to go through a textbook completely to establish some grammar fundamentals and basic concepts for Tagalog.
To sort of point you in the right direction...
1.) Yes, there are "ang", "ng" (not "nang"), and "sa" markers.
(also, the proper noun markers si/sina, ni/nina, kay/kina).
>> ang precedes the subject of the verb, and nang the object.
This is not correct, it depends on which verb you're using. You'll want to research more about how Actor Focus and Object Focus verbs work (there are other focuses as well, but those two are a good starting point).
2.) There is a very large number of affixes that can be attached to roots to make verbs, and they do change the meaning of the root/verb. Not all roots take all affix attachments. Affixes can also change the focus / structure of a sentence. There are some general guidelines about when to use which affix (for example, when mag- is more common, vs. -um-), but these should be taken with a grain of salt...this is language, not a math problem. In the end, you just have to memorize which affixes are popular in common usage, and use the same ones yourself. When you get a little more comfortable with the language, over time you'll get better at "guessing" which affixes to use in cases where you aren't sure.