(Just considering the last of your questions, “Which is the better explanation?”)
I think this is a case where the text is ambiguous as written, and so we can't work out the meaning from the grammar: instead, we have to consider each possibility and see if it makes sense in context. Grammatical ambiguity is common in Shakespeare, and often multiple readings make sense, so that the overall effect of the lines is a combination of the readings.
The first ambiguity is whether the clause “to his love and tendance” applies to “properties” only, or to both “subdues and properties”. That is, do we parse the sentence as:
- {subdues and {properties {to his love and tendance}}} {all sorts of hearts}; or
- {subdues and properties} {to his love and tendance} {all sorts of hearts}?
This ambiguity doesn’t make a difference to the meaning, because in context “subdues” and “properties” are rough synonyms, and so it doesn’t matter whether one or both of them gets the clause.
The second ambiguity is whether “his love” means “his love of them” or “their love of him”. This makes sense both ways round, depending on whether we think Timon’s “large fortune” or his “good and gracious nature” is the primary motivation. In the former case, they want Timon to love them, so that he will reward them. In the latter case, his good qualities compel them to love him. Of these readings, the first is the stronger, because the theme of the play is that people only pretend to be friends of Timon in order to get his money.
The third ambiguity is whether “his tendance” means “his attendance of them” or “their attendance of him”. In this case, the second reading is the only plausible one in context. That’s because the Poet is describing how “all minds … tender down their services to Lord Timon”, and in order for someone to tender services to Timon they must attend on him, not vice versa.
So I agree with J. H. Oliver that “his tendance” needs to be read as “their attendance of him” (the “objective genitive” interpretation), but I disagree that “his love” needs to be read as “their love of him”: I think it could be read either way, and is stronger if read as “his love of them”. I suppose that Oliver recoiled from the zeugma created by reading the phrase as “his love of them, and their attendance of him”, but I doubt that Shakespeare felt constrained by this kind of rule.