It is difficult to advise you from afar. The direct answer to your question is yes, but that is because politics can run rampant in some universities with many factions. You aren't asking whether she can be part of your formal tenure committee, I realize, but that is possible in some institutions also. Even a member from another university is a possibility.
However, having a mentor as a new faculty member can be a valuable thing, especially if you are a woman, which you don't say. At some places that mentorship can make the difference between success and failure. But a mentor needs to be pretty selfless in most respects. It is hard to interpret her request that you do research for her. That could be a good or a bad thing, depending on what you get out of the task itself. Being selfless doesn't necessarily mean that the mentor doesn't push you a bit. But, again, it is impossible to judge from here.
So, think about whether her actions are selfish or just encouragement for you to look at new things.
As for cooking and such, it is possibly worrisome unless there are some special circumstances.
But, the one piece of advice I can give is not to let your distancing be interpreted as an indication of a negative attitude, even if you have one. If you can distance and keep it neutral, then it is less likely that, in case she is selfish (or worse) that it will come back to reflect on you. Don't poke the bear in its den. But that, too, might be an unnecessary worry.
So, think first about whether she is offering mentorship and what that might mean for you in a positive way if you accept it. You might also explore her relationship to others in your institution that are in similar circumstances in order to come to a judgement on whether this is a good or a bad thing.