To take a stab at your questions, in order:

1. As far as I understand it, for Harding, standpoint theory is a re-description of objectivism. It is relativistic only inasmuch as Schwyzer lays out, that certain kinds of knowledge might be more or less difficult for particular people to have in particular socio-cultural contexts. This doesn't, it seems to me, undermine objectivism, since I don't think anyone committed to objectivism would or could deny that the process of knowledge-acquisition is a contingent one (e.g. with glasses I can identify objects better than without glasses). What would undermine objectivism, among different possible formulations, is a view that knowledge, however acquired, is not knowledge simpliciter, but is true relative to a context outside of which the truth-conditions for a claim do not obtain. This is not to say that an theory of objectivism holds that certain truth claims do not extend over particular contexts. For example, 'some apples are red' might not be true forever, and that claim, without further specification, might not be true on some other planet (but the claim could be specified sufficiently so that neither dislocation in space nor dislocation in time would change the truth value of the claim). Relativism usually, I think, reconceptualizes what knowledge and truth are enough to allow for the truth of a specific claim to be relative (e.g. a specific murder could be truly bad in the judgement of some and truly bad for others, at the same time and in the same way) or reconceptualizes what we understand at certain times and in certain ways as the pursuit of knowledge and/or truth in order to recast these pursuits as historically (potentially) noble but flawed projects that occlude how knowledge actually functions both individually and collectively.
2. This likely depends on the specific formulation of standpoint theory involved; insofar as some standpoint theories merely emphasize the contingency of knowledge acquisition and calls attention to particularly putatively important social problems I don't think that there is any essential alterity between speakers. For any formulation that would entail relativism, it could be relativism of the sort that might admit the existence of contradictions and for that reason believe in a single language of some kind (minimally, propositions); or, it could be a relativism that need not endorse contradictions per se by rejecting the possibility of a single frame that encompasses different linguistic utterances/meanings and within which they could be understood and reconciled.
3. If this question is equivalent to "Is standpoint theory a description of how knowledge-production works or is it a claim about how knowledge-production does work?", then I think it most cases it is the former, with its claim of descriptiveness entailing a normative burden insofar as if knowledge-production does work along standpoint theory lines then those seeking truth should take care to incorporate standpoint theory into their epistemologies so that truth can be better sought and easier found.

To take a stab at your questions, in order:

1. As far as I understand it, for Harding, standpoint theory is a re-description of objectivism. It is relativistic only inasmuch as Schwyzer lays out, that certain kinds of knowledge might be more or less difficult for particular people to have in particular socio-cultural contexts. This doesn't, it seems to me, undermine objectivism, since I don't think anyone committed to objectivism would or could deny that the process of knowledge-acquisition is a contingent one (e.g. with glasses I can identify objects better than without glasses). What would undermine objectivism, among different possible formulations, is a view that knowledge, however acquired, is not knowledge simpliciter, but is true relative to a context outside of which the truth-conditions for a claim do not obtain. This is not to say that an theory of objectivism holds that certain truth claims do not extend over particular contexts. For example, 'some apples are red' might not be true forever, and that claim, without further specification, might not be true on some other planet (but the claim could be specified sufficiently so that neither dislocation in space nor dislocation in time would change the truth value of the claim). Relativism usually, I think, reconceptualizes what knowledge and truth are enough to allow for the truth of a specific claim to be relative (e.g. a specific murder could be truly bad in the judgement of some and truly bad for others, at the same time and in the same way) or reconceptualizes what we understand at certain times and in certain ways as the pursuit of knowledge and/or truth in order to recast these pursuits as historically (potentially) noble but flawed projects that occlude how knowledge actually functions both individually and collectively.
2. This likely depends on the specific formulation of standpoint theory involved; insofar as some standpoint theories merely emphasize the contingency of knowledge acquisition and call attention to particularly putatively important social problems I don't think that there is any essential alterity between speakers. For any formulation that would entail relativism, it could be relativism of the sort that might admit the existence of contradictions and for that reason believe in a single language of some kind (minimally, propositions); or, it could be a relativism that need not endorse contradictions per se by rejecting the possibility of a single frame that encompasses different linguistic utterances/meanings and within which they could be understood and reconciled.
3. If this question is equivalent to "Is standpoint theory a description of how knowledge-production does work or is it a claim about how knowledge-production should work?", then I think it most cases it is both, with its claim of descriptiveness entailing a normative burden insofar as if knowledge-production does work along standpoint theory lines then those seeking truth should take care to incorporate standpoint theory into their epistemologies so that truth can be better sought and easier found.