Why Would A Company Offer Paid Suspension

While there is no way to know for sure, your guess is a reasonable one: the company is investigating or reviewing something which could have legal consequences for it, and is offering paid suspension because they don't want to potentially compound any liability of theirs with some claim by you for unpaid wages; and/or they want the "optics" (or how the situation looks) to appear more favorable to them, by showing they acted in a fair or even generous way while considering the situation.
As to advice: don't answer any questions that could potentially incriminate you or for which, to answer truthfully, you'd have to contradict other things you said or wrote earlier in the hiring process (since if you lied during the hiring process, not only could they terminate you, of course, but they could potentially sue you  for the costs they have expended in screening, interviewing, checking, hiring, etc. you). If they are asking you questions which could result in your civil or criminal liability, you may need to resign--the employer is not law enforcement, and they can't compel you to answer; you may walk away from the process, the job, and them at any time. (Though if you have already said or done anything which suggests criminal liability, they could contact the authorities about it--though are less likely to follow-up if you withdraw.)
Take and keep careful notes of anything discussed (what said, when said, by or to whom said, etc.) and keep copies of all written communications.
Innocuous questions answer truthfully, even if you've answered already, but make sure your answers are consistent: even innocent discrepancies or inconsistencies could be seized on by them as evidence of lying.
If you belong to a racial minority, or feel you are being discriminated against in some way due to race, national origin, sex, religion, age over 40, or disability, you may wish to contact the federal EEOC.