Would it be possible to ask these same professors again for recommendation letters?

Yes, it is possible.

Would they think that I look like an undecided, wavering person and thus, be reluctant to write another letter for me?

If they don't want to write another letter, they can decline. You can briefly explain what you've been up to and should explain briefly why you decided to pursue the new field of study. It's possible your recommenders might see you as having stronger skills for the new field than for law, in which case your letter might actually be stronger than before. Much of what they wrote might be general enough that they won't have to change much from the prior letter if they do choose to write you a new one.

Also, would I just candidly explain my one-year gap after my graduation in my statement of purpose?

In your statement of purpose, while not trying to hide or paper over your one-year gap, focus on why you want to move forward in the direction you're applying for. If you had experiences or learned things in that one year that helped inspire, drive, or prepare you for that field, it may be helpful to mention them. Help your reader understand why you want to work in the field you're applying for, and think about what those reasons are (esp. if you have reasons that go beyond just job prospects).

Would it be possible to ask these same professors again for recommendation letters?

Yes, it is possible.

Would they think that I look like an undecided, wavering person and thus, be reluctant to write another letter for me?

If they don't want to write another letter, they can decline. You can briefly explain what you've been up to and should explain briefly why you decided to pursue the new field of study. It's possible your recommenders might see you as having stronger skills for the new field than for law, in which case your letter might actually be stronger than before. Much of what they wrote might be general enough that they won't have to change much from the prior letter if they do choose to write you a new one.

Also, would I just candidly explain my one-year gap after my graduation in my statement of purpose?

In your statement of purpose, while not trying to hide or paper over your one-year gap, focus on why you want to move forward in the direction you're applying for. If you had experiences or learned things in that one year that helped inspire, drive, or prepare you for that field, it may be helpful to mention them. Help your reader understand why you want to work in the field you're applying for, and think about what those reasons are (esp. if you have reasons that go beyond just job prospects).