BBA

You should opt for BBA through regular college.
BBA distance has no value.

Yes ICFAI is really good option for distance education in BBA. All the best.

You should refer the following link for the same:
https://www.shiksha.com/top-10-bba-colleges-in-india-article-7797-1

It is a good university, but the fee structure is on the high side.

HR comes under hiring employees and developing their skills etc. For doing MBA, you can have any graduation degree.
Now you have a chance to do psychology, better to do it.
As Psychology is useful in all fields.

BBA in Manav Rachna is much better than any other business school as they provide us with different types of BBA courses which suits us the best. After graduation we have a range of job opportunities in various sectors of the industry. Manav Rachna also provides scholarship for students. As students

Chances of getting a good job in Gulf countries after BBA is less in comparison to seeking job after MBA. Also, it will be better if you gain few years experience before seeking a job in Gulf.

BBA is not good for anywhere except if you go for integrated MBA.

taking a break doesn't make a big impact for pursuing an MBA until you can justify what you did in the one year. this question will be asked when you go for the interview for any MBA admission . and it's preferable to go for a private institute for BBA and MBA courses.