My DLSR has no timelapse automation function, therefore I'm planning to set my camera on tripod and shot photos remotely. Is it better for camera health and/or battery to keep the camera on for hours or turn it off and on every time I want to take a photo (where 1 photo for one minute).
Honestly, I am not sure you will keep more power if you turn off the camera between shots but you will most likely have more issues by doing it.
Timelapse are best done with as much consistency as possible between shots. So any movement is potentially problematic. Already I would suggest a remote trigger rather than using the shutter-release yourself. Now, if you don't have one, you can press the shutter lightly to minimize shake but if you also have to power it on and off, I would bet that camera would move every single time.
As for power, most cameras have pretty efficient sleep modes. On many models, you can even set the sleep delay, so choose the shortest. When a DSLR powers on and off, it often uses extra power to boot and even perform a sensor cleaning cycle, so it may use more than entering and exiting sleep.
Even though yours may not have a timelapse feature, many digital cameras have an interval timer so that you can assemble the timelapse yourself but at least the shots are taken automatically. Check the manual for your camera to see if that is available.
From my experience, letting the exposure metering time out and turn itself off is the same as turning off the camera completely and there's no noticeable difference in battery drain in either case. You can tell when the metering is off when the shutter speed and aperture setting numbers disappear from the viewfinder display.
There are external triggers that can automate that for you. If you still insist taking the photos manually, be sure to at least find an external shutter release (wired or infrared) so as not to affect the composition (pressing the camera's shutter button may move the tripod slightly).
The mechanical on-off switch is certainly more endangered than the camera's internal auto-off, aside from the induced movement of the camera by using it.
I leave my cameras on all the time, often for multiple days during travel. It does not bother them; the auto-off is set to 1 min and when you touch the shutter they come back on right away. i think this is clearly the better option, and will use less battery than the full on-off cycle too.